{"id":73,"date":"2023-09-16T13:04:23","date_gmt":"2023-09-16T13:04:23","guid":{"rendered":"https:\/\/mathority.org\/ru\/%d0%bf%d1%80%d0%b8%d0%bc%d0%b5%d1%80%d1%8b-%d0%bb%d0%b8%d0%bd%d0%b5%d0%b8%d0%bd%d0%be%d0%b8-%d0%ba%d0%be%d0%bc%d0%b1%d0%b8%d0%bd%d0%b0%d1%86%d0%b8%d0%b8-%d0%b2%d0%b5%d0%ba%d1%82%d0%be%d1%80%d0%be\/"},"modified":"2023-09-16T13:04:23","modified_gmt":"2023-09-16T13:04:23","slug":"%d0%bf%d1%80%d0%b8%d0%bc%d0%b5%d1%80%d1%8b-%d0%bb%d0%b8%d0%bd%d0%b5%d0%b8%d0%bd%d0%be%d0%b8-%d0%ba%d0%be%d0%bc%d0%b1%d0%b8%d0%bd%d0%b0%d1%86%d0%b8%d0%b8-%d0%b2%d0%b5%d0%ba%d1%82%d0%be%d1%80%d0%be","status":"publish","type":"post","link":"https:\/\/mathority.org\/ru\/%d0%bf%d1%80%d0%b8%d0%bc%d0%b5%d1%80%d1%8b-%d0%bb%d0%b8%d0%bd%d0%b5%d0%b8%d0%bd%d0%be%d0%b8-%d0%ba%d0%be%d0%bc%d0%b1%d0%b8%d0%bd%d0%b0%d1%86%d0%b8%d0%b8-%d0%b2%d0%b5%d0%ba%d1%82%d0%be%d1%80%d0%be\/","title":{"rendered":"\u041b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432"},"content":{"rendered":"<p>\u041d\u0430 \u044d\u0442\u043e\u0439 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0435 \u0432\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u043e\u0431\u044a\u044f\u0441\u043d\u0435\u043d\u0438\u0435 \u0442\u043e\u0433\u043e, \u0447\u0442\u043e \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442 \u043b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u043f\u0440\u0438\u043c\u0435\u0440 \u0442\u043e\u0433\u043e, \u043a\u0430\u043a \u0432\u0435\u043a\u0442\u043e\u0440 \u0432\u044b\u0440\u0430\u0436\u0430\u0435\u0442\u0441\u044f \u0432 \u0432\u0438\u0434\u0435 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u0438, \u0438, \u043a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u043f\u043e\u043f\u0440\u0430\u043a\u0442\u0438\u043a\u043e\u0432\u0430\u0442\u044c\u0441\u044f \u0441 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f\u043c\u0438 \u0438 \u0437\u0430\u0434\u0430\u0447\u0430\u043c\u0438, \u0440\u0435\u0448\u0430\u0435\u043c\u044b\u043c\u0438 \u0448\u0430\u0433 \u0437\u0430 \u0448\u0430\u0433\u043e\u043c. <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-104\"><\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-combinacion-lineal-de-vectores\"><\/span> \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u0438 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435: <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-105\"><\/div>\n<\/div>\n<div style=\"background-color:#FFCC8080;padding-top: 20px; padding-bottom: 0.5px; padding-right: 40px; padding-left: 30px; border: 2px solid #FFB74D; border-radius:20px;\">\n<p style=\"text-align:left\"> <strong>\u041b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044f<\/strong> \u043d\u0430\u0431\u043e\u0440\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u2014 \u044d\u0442\u043e \u0432\u0435\u043a\u0442\u043e\u0440, \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u044b\u0439 \u0441\u043b\u043e\u0436\u0435\u043d\u0438\u0435\u043c \u0432\u0441\u0435\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u043d\u0430\u0431\u043e\u0440\u0430, \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u043d\u044b\u043c\u0438 \u043d\u0430 \u0441\u043a\u0430\u043b\u044f\u0440\u044b (\u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u0447\u0438\u0441\u043b\u0430).<\/p>\n<p style=\"text-align:left\"> \u0414\u0440\u0443\u0433\u0438\u043c\u0438 \u0441\u043b\u043e\u0432\u0430\u043c\u0438, \u0434\u043b\u044f \u0434\u0430\u043d\u043d\u043e\u0433\u043e \u043d\u0430\u0431\u043e\u0440\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-33729e6d20b00643b5d9ddf38544c11c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}_1, \\vv{\\text{v}}_2,\\ldots \\vv{\\text{v}}_n,\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"96\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u0438\u0445 \u043b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044f \u0431\u0443\u0434\u0435\u0442:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a1fe2e85f82aa1452aa43a172ca8d256_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{w}}=a_1\\vv{\\text{v}}_1+a_2\\vv{\\text{v}}_2+\\dots + a_n\\vv{\\text{v}}_n\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"226\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\"> \u0413\u0434\u0435 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f91083f3035e5168a6f0b3e6335d6858_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"14\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u042d\u0442\u043e \u0440\u0435\u0430\u043b\u044c\u043d\u044b\u0435 \u0446\u0438\u0444\u0440\u044b.<\/p>\n<\/div>\n<p> \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0432\u0435\u043a\u0442\u043e\u0440, \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0449\u0438\u0439 \u0441\u043e\u0431\u043e\u0439 \u043b\u0438\u043d\u0435\u0439\u043d\u0443\u044e \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044e \u0434\u0440\u0443\u0433\u0438\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432, \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e \u043f\u0435\u0440\u0432\u044b\u0439 \u043c\u043e\u0436\u043d\u043e \u0432\u044b\u0440\u0430\u0437\u0438\u0442\u044c \u0447\u0435\u0440\u0435\u0437 \u0432\u0442\u043e\u0440\u043e\u0439.<\/p>\n<p> \u042d\u0442\u0443 \u043a\u043e\u043d\u0446\u0435\u043f\u0446\u0438\u044e \u043c\u043e\u0436\u043d\u043e \u043b\u0443\u0447\u0448\u0435 \u043f\u043e\u043d\u044f\u0442\u044c, \u043f\u043e\u0441\u0442\u0440\u043e\u0438\u0432 \u0433\u0440\u0430\u0444\u0438\u043a \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043d\u0430 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043e\u0431\u043e\u0439 \u043b\u0438\u043d\u0435\u0439\u043d\u0443\u044e \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044e \u0434\u0432\u0443\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/combinaison-lineaire-de-vecteurs-graphique.webp\" alt=\"\u043b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u0432 r3\" class=\"wp-image-781\" width=\"405\" height=\"408\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> \u041a\u0430\u043a \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u0432\u0438\u0434\u0435\u0442\u044c \u043d\u0430 \u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u043e\u043c \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u0438 \u0432\u044b\u0448\u0435, \u0432\u0435\u043a\u0442\u043e\u0440<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3b4bbbc56786695092eac40831aee80d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{w}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u043c\u043e\u0436\u043d\u043e \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u0438\u0437 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cac24ae79c1e4cbc459f01ed5e4f824e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0418<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-391ac2e3ba0b7f327ba5a0edc1ba162d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0442\u044c \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u044b\u0435 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0432\u0435\u043a\u0442\u043e\u0440<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3b4bbbc56786695092eac40831aee80d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{w}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043e\u0431\u043e\u0439 \u043b\u0438\u043d\u0435\u0439\u043d\u0443\u044e \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044e \u0434\u0432\u0443\u0445 \u0434\u0440\u0443\u0433\u0438\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432.<\/p>\n<p> \u0421\u043b\u0435\u0434\u0443\u0435\u0442 \u043f\u043e\u0434\u0447\u0435\u0440\u043a\u043d\u0443\u0442\u044c, \u0447\u0442\u043e \u044d\u0442\u0430 \u043b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044f <strong>\u0443\u043d\u0438\u043a\u0430\u043b\u044c\u043d\u0430<\/strong> , \u0438\u043b\u0438, \u0434\u0440\u0443\u0433\u0438\u043c\u0438 \u0441\u043b\u043e\u0432\u0430\u043c\u0438, \u0434\u043b\u044f \u043a\u0430\u0436\u0434\u043e\u0433\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0442\u043e\u043b\u044c\u043a\u043e \u043e\u0434\u043d\u0430 \u0434\u043e\u043f\u0443\u0441\u0442\u0438\u043c\u0430\u044f \u043b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044f. \u041f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443, \u0441\u043b\u0435\u0434\u0443\u044f \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u043c\u0443 \u043f\u0440\u0438\u043c\u0435\u0440\u0443, \u0435\u0441\u043b\u0438 \u043c\u044b \u0443\u043c\u043d\u043e\u0436\u0438\u043b\u0438<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cac24ae79c1e4cbc459f01ed5e4f824e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0434\u043b\u044f 6 \u0432\u043c\u0435\u0441\u0442\u043e 4 \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u043c \u0434\u0440\u0443\u0433\u043e\u0439 \u0432\u0435\u043a\u0442\u043e\u0440. <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-106\"><\/div>\n<\/div>\n<p> \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u043e\u0434\u043d\u043e \u0438\u0437 \u0441\u0432\u043e\u0439\u0441\u0442\u0432 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u0438 \u043d\u0430 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 (\u0432 R2) \u0441\u043e\u0441\u0442\u043e\u0438\u0442 \u0432 \u0442\u043e\u043c, \u0447\u0442\u043e \u043b\u044e\u0431\u043e\u0439 \u0432\u0435\u043a\u0442\u043e\u0440 \u043c\u043e\u0436\u043d\u043e \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0438\u0442\u044c \u043a\u0430\u043a \u043b\u0438\u043d\u0435\u0439\u043d\u0443\u044e \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044e \u0434\u0432\u0443\u0445 \u0434\u0440\u0443\u0433\u0438\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432, \u0435\u0441\u043b\u0438 \u043e\u043d\u0438 \u0438\u043c\u0435\u044e\u0442 \u0440\u0430\u0437\u043d\u044b\u0435 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u044f, \u0442. \u0435. \u0435\u0441\u043b\u0438 \u043e\u043d\u0438 \u043d\u0435 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b.<\/p>\n<p> \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0438\u043d\u043e\u0433\u0434\u0430 \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u043d\u0430 \u0433\u043b\u0430\u0437 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c, \u0447\u0442\u043e \u0434\u0432\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0442 \u0441\u043e\u0431\u043e\u0439 \u043b\u0438\u043d\u0435\u0439\u043d\u0443\u044e \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044e. \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u0434\u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u043e, \u0447\u0442\u043e\u0431\u044b \u0435\u0433\u043e \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u044b \u0431\u044b\u043b\u0438 <strong>\u043f\u0440\u043e\u043f\u043e\u0440\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b<\/strong> . \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0445 \u0434\u0432\u0443\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u043f\u0440\u043e\u043f\u043e\u0440\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b \u0438, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0432\u0435\u043a\u0442\u043e\u0440\u044b \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0442 \u0441\u043e\u0431\u043e\u0439 \u043b\u0438\u043d\u0435\u0439\u043d\u0443\u044e \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044e:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f7e90b69f6225543322e762773bbe775_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (1,2,-1) \\qquad \\vv{\\text{v}} = (3,6,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"241\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-aac41542948764e158ebe590c6b36e67_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{3}{1} = \\cfrac{6}{2} = \\cfrac{-3}{-1} = 3 \\ \\longrightarrow \\ \\text{Proporcionales}\\ \\longrightarrow \\ \\begin{array}{c} \\text{Combinaci\\'on}\\\\[2ex] \\text{lineal} \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"51\" width=\"456\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u0435\u0441\u043b\u0438 \u0432 \u0434\u0432\u0443\u043c\u0435\u0440\u043d\u043e\u043c (\u0432 R2) \u0438\u043b\u0438 \u0442\u0440\u0435\u0445\u043c\u0435\u0440\u043d\u043e\u043c (\u0432 R3) \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u043c \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u043b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044f \u0432\u043d\u0443\u0442\u0440\u0438 \u043d\u0430\u0431\u043e\u0440\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432, \u044d\u0442\u043e \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e \u043e\u043d\u0438 <strong>\u043b\u0438\u043d\u0435\u0439\u043d\u043e \u0437\u0430\u0432\u0438\u0441\u044f\u0442<\/strong> \u0434\u0440\u0443\u0433 \u043e\u0442 \u0434\u0440\u0443\u0433\u0430. \u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u0435\u0441\u043b\u0438 \u043c\u0435\u0436\u0434\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c\u0438 \u043d\u0435\u0432\u043e\u0437\u043c\u043e\u0436\u043d\u0430 \u043b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044f, \u044d\u0442\u043e \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e \u043e\u043d\u0438 <strong>\u043b\u0438\u043d\u0435\u0439\u043d\u043e \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b<\/strong> .<\/p>\n<p> \u0415\u0441\u043b\u0438 \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0435\u0435 \u043f\u043e\u043d\u044f\u0442\u0438\u0435 \u0432\u0430\u043c \u043d\u0435 \u0441\u043e\u0432\u0441\u0435\u043c \u043f\u043e\u043d\u044f\u0442\u043d\u043e, \u0440\u0435\u043a\u043e\u043c\u0435\u043d\u0434\u0443\u0435\u043c \u043e\u0437\u043d\u0430\u043a\u043e\u043c\u0438\u0442\u044c\u0441\u044f \u0441 \u043d\u0430\u0448\u0438\u043c \u043e\u0431\u044a\u044f\u0441\u043d\u0435\u043d\u0438\u0435\u043c  \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u0445 \u0438 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432  , \u0437\u0434\u0435\u0441\u044c \u0432\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435, \u0447\u0442\u043e \u0437\u043d\u0430\u0447\u0438\u0442 \u0434\u043b\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u0431\u044b\u0442\u044c \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u043c\u0438 \u0438\u043b\u0438 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u043c\u0438, \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u043a\u0430\u0436\u0434\u043e\u0433\u043e \u0442\u0438\u043f\u0430 \u0438 \u0440\u0430\u0437\u043b\u0438\u0447\u0438\u044f \u043c\u0435\u0436\u0434\u0443 \u043d\u0438\u043c\u0438. . \u042d\u0442\u043e \u043f\u043e\u043d\u044f\u0442\u0438\u0435 \u0447\u0430\u0441\u0442\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u0438, \u043d\u0430 \u0441\u0430\u043c\u043e\u043c \u0434\u0435\u043b\u0435, \u0435\u0433\u043e \u0447\u0430\u0441\u0442\u043e \u0437\u0430\u0434\u0430\u044e\u0442 \u043d\u0430 \u044d\u043a\u0437\u0430\u043c\u0435\u043d\u0430\u0445, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0432\u0430\u0436\u043d\u043e, \u0447\u0442\u043e\u0431\u044b \u0432\u044b \u0435\u0433\u043e \u0445\u043e\u0440\u043e\u0448\u043e \u043f\u043e\u043d\u044f\u043b\u0438. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-expresar-un-vector-como-combinacion-lineal-de-otros-vectores\"><\/span> \u041a\u0430\u043a \u0432\u044b\u0440\u0430\u0437\u0438\u0442\u044c \u0432\u0435\u043a\u0442\u043e\u0440 \u043a\u0430\u043a \u043b\u0438\u043d\u0435\u0439\u043d\u0443\u044e \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044e \u0434\u0440\u0443\u0433\u0438\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-109\"><\/div>\n<\/div>\n<p> \u0417\u0430\u0442\u0435\u043c \u043c\u044b \u0443\u0432\u0438\u0434\u0438\u043c, \u043a\u0430\u043a \u0440\u0435\u0448\u0438\u0442\u044c \u0442\u0438\u043f\u0438\u0447\u043d\u0443\u044e \u0437\u0430\u0434\u0430\u0447\u0443, \u0432 \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u043d\u0430\u0441 \u043f\u0440\u043e\u0441\u044f\u0442 \u043d\u0430\u0439\u0442\u0438 \u043b\u0438\u043d\u0435\u0439\u043d\u0443\u044e \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044e \u0432\u0435\u043a\u0442\u043e\u0440\u0430.<\/p>\n<ul>\n<li> \u0412\u044b\u0440\u0430\u0437\u0438\u0442\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-88e41d561c3898029b7b94d7014c1e79_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u043a\u0430\u043a \u043b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044f<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4b6be5a59bbf478047e4f3ace338ee48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}, \\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"27\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u0418 <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d8af8ced46d93e73dc5290e0cca4dc6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{w}}.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"17\" style=\"vertical-align: 0px;\"><\/p>\n<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7c6a832874f83ba4de52e88fdd6ed48a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{x}} = (3,1,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"88\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-746bff339baec38ef705a9ede42411cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (1,0,1) \\qquad \\vv{\\text{v}} = (1,2,0) \\qquad \\vv{\\text{w}} = (0,1,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"355\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0422\u0430\u043a \u0447\u0442\u043e \u0432\u0435\u043a\u0442\u043e\u0440<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-88e41d561c3898029b7b94d7014c1e79_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0431\u044b\u0442\u044c \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u0435\u0439 \u0434\u0440\u0443\u0433\u0438\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432, \u0434\u043e\u043b\u0436\u043d\u043e \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0442\u044c\u0441\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-06d3d6ec5ca4921b109f8f974e73cbbd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1\\vv{\\text{u}}+a_2\\vv{\\text{v}}+ a_3\\vv{\\text{w}}=\\vv{\\text{x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"160\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p> \u0413\u0434\u0435 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-41a350e61a3992febcf5f69fdb79f79a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1, a_2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"41\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u0418<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a4306749a1a62a769b17b849d10edba8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_3\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u042d\u0442\u043e \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u0435, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043c\u044b \u0434\u043e\u043b\u0436\u043d\u044b \u043d\u0430\u0439\u0442\u0438.<\/p>\n<p> \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u0437\u0430\u043c\u0435\u043d\u044f\u0435\u043c \u043a\u0430\u0436\u0434\u044b\u0439 \u0432\u0435\u043a\u0442\u043e\u0440 \u0435\u0433\u043e \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0430\u043c\u0438:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d9ed95a00184b48d358ba1b0a2abf105_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1\\begin{pmatrix} 1 \\\\0\\\\1 \\end{pmatrix}+a_2\\begin{pmatrix} 1 \\\\2\\\\0 \\end{pmatrix}+ a_3\\begin{pmatrix} 0 \\\\1\\\\-1 \\end{pmatrix}=\\begin{pmatrix} 3 \\\\1\\\\2 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"64\" width=\"296\" style=\"vertical-align: -27px;\"><\/p>\n<\/p>\n<p> \u0423\u043c\u043d\u043e\u0436\u0430\u0435\u043c \u043a\u0430\u0436\u0434\u044b\u0439 \u0432\u0435\u043a\u0442\u043e\u0440 \u043d\u0430 \u0435\u0433\u043e \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-626790fc18c5942db14924be2397c9f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix} a_1 \\\\0\\\\a_1 \\end{pmatrix}+\\begin{pmatrix} a_2 \\\\2a_2\\\\0 \\end{pmatrix}+ \\begin{pmatrix} 0 \\\\a_3\\\\-a_3 \\end{pmatrix}=\\begin{pmatrix} 3 \\\\1\\\\2 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"64\" width=\"264\" style=\"vertical-align: -27px;\"><\/p>\n<\/p>\n<p> \u0414\u043e\u0431\u0430\u0432\u043b\u044f\u0435\u043c \u0432\u0435\u043a\u0442\u043e\u0440\u044b:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1f8ab5661ba692df579d8e88b6244cdd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix} a_1 +a_2\\\\2a_2+a_3\\\\a_1-a_3 \\end{pmatrix}=\\begin{pmatrix} 3 \\\\1\\\\2 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"64\" width=\"150\" style=\"vertical-align: -27px;\"><\/p>\n<\/p>\n<p> \u041a\u0430\u0436\u0434\u0430\u044f \u043b\u0435\u0432\u0430\u044f \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0430 \u0434\u043e\u043b\u0436\u043d\u0430 \u0431\u044b\u0442\u044c \u0440\u0430\u0432\u043d\u0430 \u043a\u0430\u0436\u0434\u043e\u0439 \u043f\u0440\u0430\u0432\u043e\u0439 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0435. \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0443 \u043d\u0430\u0441 \u0435\u0441\u0442\u044c 3 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8e5fe050102a285a325dcd81d07ef5d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{l} a_1 +a_2 = 3 \\\\[2ex] 2a_2+a_3 =1\\\\[2ex] a_1-a_3 = 2 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"118\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u041e\u0441\u0442\u0430\u0435\u0442\u0441\u044f \u0442\u043e\u043b\u044c\u043a\u043e \u0440\u0435\u0448\u0438\u0442\u044c \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u0443\u044e \u0441\u0438\u0441\u0442\u0435\u043c\u0443 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439. \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0439\u0442\u0435 \u043f\u0440\u0435\u0434\u043f\u043e\u0447\u0438\u0442\u0430\u0435\u043c\u044b\u0439 \u0432\u0430\u043c\u0438 \u043c\u0435\u0442\u043e\u0434 (\u043c\u0435\u0442\u043e\u0434 \u0437\u0430\u043c\u0435\u043d\u044b, \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u041a\u0440\u0430\u043c\u0435\u0440\u0430, \u043c\u0435\u0442\u043e\u0434 \u0413\u0430\u0443\u0441\u0441\u0430-\u0416\u043e\u0440\u0434\u0430\u043d\u0430 \u0438 \u0442. \u0434.), \u0432 \u0434\u0430\u043d\u043d\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0432\u043e\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c\u0441\u044f \u043c\u0435\u0442\u043e\u0434\u043e\u043c \u0413\u0430\u0443\u0441\u0441\u0430: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8aa4e245614f286e0697797a18ba4465_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} 1&amp;1&amp;0&amp; 3 \\\\[2ex] 0&amp;2&amp;1&amp;1\\\\[2ex] 1&amp;0&amp;-1&amp;2 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"135\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-41f1d9c941fe239bb40297b998eb6929_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(\\begin{array}{ccc|c} 1&amp;1&amp;0&amp; 3 \\\\[2ex] 0&amp;2&amp;1&amp;1\\\\[2ex] 1&amp;0&amp;-1&amp;2 \\end{array} \\right) \\begin{array}{c} \\\\[2ex] \\\\[2ex] \\xrightarrow{F_3-F_1} \\end{array} \\left( \\begin{array}{ccc|c} 1&amp;1&amp;0&amp; 3 \\\\[2ex] 0&amp;2&amp;1&amp;1\\\\[2ex] 0&amp;-1&amp;-1&amp;-1 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"382\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-02a8a00406479f367627b682099e05c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} 1&amp;1&amp;0&amp; 3 \\\\[2ex] 0&amp;2&amp;1&amp;1\\\\[2ex] 0&amp;-1&amp;-1&amp;-1 \\end{array} \\right)\\begin{array}{c} \\\\[2ex] \\\\[2ex] \\xrightarrow{2F_3+F_2}\\end{array} \\left( \\begin{array}{ccc|c} 1&amp;1&amp;0&amp; 3 \\\\[2ex] 0&amp;2&amp;1&amp;1\\\\[2ex] 0&amp;0&amp;-1&amp;-1 \\end{array}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"403\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u0430\u044f \u0441\u0438\u0441\u0442\u0435\u043c\u0430 \u0448\u0430\u0433\u043e\u0432 \u0442\u0430\u043a\u043e\u0432\u0430:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-74ed1b18779582d6683ecaa1a9085e3d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{r} a_1 +a_2 = 3 \\\\[2ex] 2a_2+a_3 =1\\\\[2ex] -a_3 = -1 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"118\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0412\u0441\u0435, \u0447\u0442\u043e \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u0441\u0434\u0435\u043b\u0430\u0442\u044c \u0441\u0435\u0439\u0447\u0430\u0441, \u044d\u0442\u043e \u043f\u0440\u043e\u044f\u0441\u043d\u0438\u0442\u044c \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e\u0435 \u0438 \u043d\u0430\u0439\u0442\u0438 \u0435\u0433\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435. \u0418\u0442\u0430\u043a, \u0438\u0437 \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0435\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043d\u0430\u0445\u043e\u0434\u0438\u043c<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a5e5ed86162a9b0324b8f44dc16fcbce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_3:\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"26\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a9098f1754f21ebdb169710a81771238_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-a_3 = -1 \\ \\longrightarrow \\ \\bm{a_3 = 1}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"175\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p> \u0418\u0437 \u0432\u0442\u043e\u0440\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0441\u0438\u0441\u0442\u0435\u043c\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2789190f1df15f5bd570b643d9bb29f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_2:\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"26\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5d375653cd224859cfb1172eff34b13a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2a_2+a_3 =1 \\ \\xrightarrow{a_3\\ = \\ 1} \\ 2a_2+1=1\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"261\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cd6833a5f5007dec00e1b7a1c0820bd9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2a_2=1-1\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"88\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-aa265a6ea06995349079b84bfae9d627_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2a_2=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"59\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0d26904a10ba1c4d37589b41962c6b9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{a_2=0}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"50\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p> \u0418, \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u0438\u0437 \u043f\u0435\u0440\u0432\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0441\u0438\u0441\u0442\u0435\u043c\u044b \u0448\u0430\u0433\u043e\u0432 \u043d\u0430\u0445\u043e\u0434\u0438\u043c \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u0443\u044e<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c80696de686104689a20cb70c0033830_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1:\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"26\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9506e180ee4e8b7a69fa509b823fdcca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1 +a_2 = 3 \\ \\xrightarrow{a_3\\ = \\ 1 \\ ; \\ a_2 \\ = \\ 0 } \\ \\bm{a_1 = 3}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"273\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u0441\u0438\u0441\u0442\u0435\u043c\u044b \u043b\u0438\u043d\u0435\u0439\u043d\u044b\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u0438\u043c\u0435\u0435\u0442 \u0432\u0438\u0434:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f27368cbdc2111d5e30c1c29c5da8f95_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1=3 \\qquad a_2=0 \\qquad a_3 = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"219\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p> \u0418\u0442\u0430\u043a, \u0432\u0435\u043a\u0442\u043e\u0440<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-88e41d561c3898029b7b94d7014c1e79_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0415\u0433\u043e \u043c\u043e\u0436\u043d\u043e \u0432\u044b\u0440\u0430\u0437\u0438\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u0435\u0439: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-80aba06b670bf9eedd4074be0750c3d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{x}}= a_1\\vv{\\text{u}}+a_2\\vv{\\text{v}}+ a_3\\vv{\\text{w}}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"160\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0cad8a3d5bdbe0461d347a8a3f21f794_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{x}}= 3\\vv{\\text{u}}+0\\vv{\\text{v}}+ 1\\vv{\\text{w}}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"135\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8ccdc9d2a3852c38c4442d0b601b6644_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\mathbf{x}}\\bm{= 3}\\vv{\\mathbf{u}} \\bm{+} \\vv{\\mathbf{w}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"78\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043c\u0435\u0436\u0434\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c\u0438 \u0444\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u043b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c. \u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u0435\u0441\u043b\u0438 \u0431\u044b \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u0441\u0438\u0441\u0442\u0435\u043c\u044b \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u043d\u0435 \u0431\u044b\u043b\u043e \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043e, \u044d\u0442\u043e \u043e\u0437\u043d\u0430\u0447\u0430\u043b\u043e \u0431\u044b, \u0447\u0442\u043e \u0432\u0435\u043a\u0442\u043e\u0440<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-88e41d561c3898029b7b94d7014c1e79_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u041e\u043d \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c \u043f\u043e \u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u044e \u043a \u0434\u0440\u0443\u0433\u0438\u043c \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c, \u0438, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043d\u0435 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e\u0439 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u0438 \u0434\u043b\u044f \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438\u044f \u0443\u043a\u0430\u0437\u0430\u043d\u043d\u043e\u0433\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u0438\u0437 \u0434\u0440\u0443\u0433\u0438\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-combinacion-lineal-de-vectores\"><\/span> \u0420\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f \u043d\u0430 \u043b\u0438\u043d\u0435\u0439\u043d\u0443\u044e \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044e \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> \u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 1<\/h3>\n<p> \u0421\u0440\u0435\u0434\u0438 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0445 \u0442\u0440\u0435\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u0443\u043a\u0430\u0436\u0438\u0442\u0435, \u043a\u0430\u043a\u0438\u0435 \u043f\u0430\u0440\u044b \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u043b\u0438\u043d\u0435\u0439\u043d\u044b\u043c\u0438 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044f\u043c\u0438 \u0434\u0440\u0443\u0433 \u0434\u0440\u0443\u0433\u0430. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u043d\u0430\u0439\u0434\u0438\u0442\u0435 \u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u0435 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u0438 \u0443\u043a\u0430\u0437\u0430\u043d\u043d\u044b\u0445 \u043f\u0430\u0440 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432. <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0558431e1c2e3040ed06e8bd04be0d3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (2,4,3) \\qquad \\vv{\\text{v}} = (1,2,-3) \\qquad \\vv{\\text{w}} = (-3,-6,9)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"383\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u0427\u0442\u043e\u0431\u044b \u0443\u0437\u043d\u0430\u0442\u044c, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043b\u0438 \u043f\u0430\u0440\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u0435\u0439, \u043c\u044b \u0434\u043e\u043b\u0436\u043d\u044b \u043f\u0440\u043e\u0432\u0435\u0440\u0438\u0442\u044c, \u043f\u0440\u043e\u043f\u043e\u0440\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b \u043b\u0438 \u0438\u0445 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b.<\/p>\n<p class=\"has-text-align-left\"> \u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u043f\u0440\u043e\u0432\u0435\u0440\u044f\u0435\u043c \u0432\u0435\u043a\u0442\u043e\u0440<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cac24ae79c1e4cbc459f01ed5e4f824e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0441 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u043c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8f5713006a9840d2d71efbe7b540d21a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}} :\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"18\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fc4cadf576dfcd515bba9e31c113c317_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{2}{1} = \\cfrac{4}{2} \\neq \\cfrac{3}{-3} \\ \\longrightarrow \\ \\text{No proporcionales}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"283\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0412\u043e-\u0432\u0442\u043e\u0440\u044b\u0445, \u043c\u044b \u043f\u0440\u043e\u0432\u0435\u0440\u044f\u0435\u043c \u0432\u0435\u043a\u0442\u043e\u0440<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cac24ae79c1e4cbc459f01ed5e4f824e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0441 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u043c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-97cea7925862c08ac4cf5b4963c0187b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{w}} :\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"22\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ccc5afad1474f92824813625a0f04242_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{2}{-3} = \\cfrac{4}{-6} \\neq \\cfrac{3}{9} \\ \\longrightarrow \\ \\text{No proporcionales}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"297\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u043c\u044b \u043f\u0440\u043e\u0432\u0435\u0440\u044f\u0435\u043c \u0432\u0435\u043a\u0442\u043e\u0440<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-391ac2e3ba0b7f327ba5a0edc1ba162d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0441 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u043c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-97cea7925862c08ac4cf5b4963c0187b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{w}} :\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"22\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f818eb5ae0825dd43290331519599c21_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{1}{-3} = \\cfrac{2}{-6} = \\cfrac{-3}{9} = -\\cfrac{1}{3} \\ \\longrightarrow \\ \\text{Proporcionales}\\ \\longrightarrow \\ \\begin{array}{c} \\text{Combinaci\\'on}\\\\[2ex] \\text{lineal} \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"51\" width=\"499\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0435\u0434\u0438\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u0430\u044f \u043f\u0430\u0440\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432, \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0449\u0430\u044f \u0441\u043e\u0431\u043e\u0439 \u043b\u0438\u043d\u0435\u0439\u043d\u0443\u044e \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044e, \u2014 \u044d\u0442\u043e<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-391ac2e3ba0b7f327ba5a0edc1ba162d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0418<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d8af8ced46d93e73dc5290e0cca4dc6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{w}}.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"17\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0411\u043e\u043b\u0435\u0435 \u0442\u043e\u0433\u043e, \u0438\u0445 \u0432\u0437\u0430\u0438\u043c\u043e\u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u044f \u0442\u0430\u043a\u043e\u0432\u044b:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ca9417b2ef9db0db6d78c0af39dde0b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}= -\\cfrac{1}{3} \\vv{\\text{w}}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"71\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0418\u043b\u0438 \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-69433589474e50574aa5d9dcbd188b28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{w}}= -3 \\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"68\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0425\u043e\u0442\u044f \u0443\u0442\u0432\u0435\u0440\u0436\u0434\u0435\u043d\u0438\u0435 \u044d\u0442\u043e\u0433\u043e \u043d\u0435 \u0442\u0440\u0435\u0431\u0443\u0435\u0442, \u0435\u0434\u0438\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u043c\u0438 \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c\u0438, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u0437\u0430\u0432\u0438\u0441\u044f\u0442 \u0434\u0440\u0443\u0433 \u043e\u0442 \u0434\u0440\u0443\u0433\u0430, \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-391ac2e3ba0b7f327ba5a0edc1ba162d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0418<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3b4bbbc56786695092eac40831aee80d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{w}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u043f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e \u043c\u0435\u0436\u0434\u0443 \u043d\u0438\u043c\u0438 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u043b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044f. \u041e\u0441\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u043f\u0430\u0440\u044b \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0438\u0445 \u043d\u0435\u043b\u044c\u0437\u044f \u043e\u0431\u044a\u0435\u0434\u0438\u043d\u0438\u0442\u044c \u043b\u0438\u043d\u0435\u0439\u043d\u043e.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> \u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 2<\/h3>\n<p> \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u043b\u0438\u043d\u0435\u0439\u043d\u0443\u044e \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u043c\u0435\u0436\u0434\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u043c<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-88e41d561c3898029b7b94d7014c1e79_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0438 \u043d\u0430\u0431\u043e\u0440 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4b6be5a59bbf478047e4f3ace338ee48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}, \\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"27\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u0418 <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d8af8ced46d93e73dc5290e0cca4dc6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{w}}.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"17\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0c010556cb8d46303e7253102ef28e47_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{x}} = (4,2,5)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"88\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-88611544e069c7a373363f2f708dcd8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (1,-1,0) \\qquad \\vv{\\text{v}} = (1,2,2) \\qquad \\vv{\\text{w}} = (-1,1,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"383\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u0422\u0430\u043a \u0447\u0442\u043e \u0432\u0435\u043a\u0442\u043e\u0440<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-88e41d561c3898029b7b94d7014c1e79_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0431\u044b\u0442\u044c \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u0435\u0439 \u0434\u0440\u0443\u0433\u0438\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432, \u0434\u043e\u043b\u0436\u043d\u043e \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0442\u044c\u0441\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-06d3d6ec5ca4921b109f8f974e73cbbd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1\\vv{\\text{u}}+a_2\\vv{\\text{v}}+ a_3\\vv{\\text{w}}=\\vv{\\text{x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"160\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u0437\u0430\u043c\u0435\u043d\u044f\u0435\u043c \u043a\u0430\u0436\u0434\u044b\u0439 \u0432\u0435\u043a\u0442\u043e\u0440 \u0435\u0433\u043e \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0430\u043c\u0438:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1b5da9716a3ae4f55bf8997927615f71_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1\\begin{pmatrix} 1 \\\\-1\\\\0 \\end{pmatrix}+a_2\\begin{pmatrix} 1 \\\\2\\\\2 \\end{pmatrix}+ a_3\\begin{pmatrix} -1 \\\\1\\\\-1 \\end{pmatrix}=\\begin{pmatrix} 4 \\\\2\\\\5 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"64\" width=\"310\" style=\"vertical-align: -27px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0423\u043c\u043d\u043e\u0436\u0438\u043c \u043a\u0430\u0436\u0434\u044b\u0439 \u0432\u0435\u043a\u0442\u043e\u0440 \u043d\u0430 \u0435\u0433\u043e \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u0443:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ea9db980d051c022dc56036cd96b054f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix} a_1 \\\\-a_1\\\\0 \\end{pmatrix}+\\begin{pmatrix} a_2 \\\\2a_2\\\\2a_2 \\end{pmatrix}+ \\begin{pmatrix} -a_3 \\\\a_3\\\\-a_3 \\end{pmatrix}=\\begin{pmatrix} 4 \\\\2\\\\5 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"64\" width=\"278\" style=\"vertical-align: -27px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0414\u043e\u0431\u0430\u0432\u043b\u044f\u0435\u043c \u0432\u0435\u043a\u0442\u043e\u0440\u044b:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8e0fc02c135530814884b62685cc22b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix} a_1 +a_2-a_3\\\\-a_1+2a_2+a_3\\\\ 2a_2-a_3 \\end{pmatrix}=\\begin{pmatrix} 4 \\\\2\\\\5 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"64\" width=\"202\" style=\"vertical-align: -27px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0443\u044e \u0441\u0438\u0441\u0442\u0435\u043c\u0443 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1ea3ca998fc7d9d9b2cf42d43a5bf0a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{l} a_1 +a_2-a_3 = 4 \\\\[2ex] -a_1+2a_2+a_3 =2\\\\[2ex] 2a_2-a_3 = 5 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"171\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0420\u0435\u0448\u0430\u0435\u043c \u0441\u0438\u0441\u0442\u0435\u043c\u0443, \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u0443\u044e \u043c\u0435\u0442\u043e\u0434\u043e\u043c \u0413\u0430\u0443\u0441\u0441\u0430: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c808441bc71bd26e333ebe2169b738ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} 1&amp;1&amp;-1&amp; 4 \\\\[2ex] -1&amp;2&amp;1&amp;2\\\\[2ex] 0&amp;2&amp;-1&amp;5 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"149\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-941792a2de155bc284b14e34dc561418_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(\\begin{array}{ccc|c} 1&amp;1&amp;-1&amp; 4 \\\\[2ex] -1&amp;2&amp;1&amp;2\\\\[2ex] 0&amp;2&amp;-1&amp;5 \\end{array} \\right) \\begin{array}{c} \\\\[2ex] \\xrightarrow{F_2+F_1}\\\\[2ex] &amp; \\end{array} \\left( \\begin{array}{ccc|c} 1&amp;1&amp;-1&amp; 4 \\\\[2ex] 0&amp;3&amp;0&amp;6\\\\[2ex] 0&amp;2&amp;-1&amp;5\\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"369\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7105de2fa579f40818bccc2df48961ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(\\begin{array}{ccc|c} 1&amp;1&amp;-1&amp; 4 \\\\[2ex] 0&amp;3&amp;0&amp;6\\\\[2ex] 0&amp;2&amp;-1&amp;5 \\end{array} \\right) \\begin{array}{c} \\\\[2ex] \\\\[2ex] \\xrightarrow{3F_3-2F_2} \\end{array} \\left( \\begin{array}{ccc|c} 1&amp;1&amp;-1&amp; 4 \\\\[2ex] 0&amp;3&amp;0&amp;6\\\\[2ex] 0&amp;0&amp;-3&amp;3\\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"369\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u0430\u044f \u0441\u0438\u0441\u0442\u0435\u043c\u0430 \u0448\u0430\u0433\u043e\u0432 \u0442\u0430\u043a\u043e\u0432\u0430:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bfd5b2d564f66cd225c1a5987241ba14_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{r} a_1 +a_2-a_3 = 4 \\\\[2ex] 3a_2 =6\\\\[2ex] -3a_3 = 3 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"148\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0412\u0441\u0435, \u0447\u0442\u043e \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u0441\u0434\u0435\u043b\u0430\u0442\u044c \u0441\u0435\u0439\u0447\u0430\u0441, \u044d\u0442\u043e \u043f\u0440\u043e\u044f\u0441\u043d\u0438\u0442\u044c \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e\u0435 \u0438 \u043d\u0430\u0439\u0442\u0438 \u0435\u0433\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435. \u0418\u0442\u0430\u043a, \u0438\u0437 \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0435\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043d\u0430\u0445\u043e\u0434\u0438\u043c <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a5e5ed86162a9b0324b8f44dc16fcbce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_3:\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"26\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-667fa5894272768e2e53f618a9752611_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-3a_3 = 3\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"71\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9b4234a97996e589d5d34b629a19bd0c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_3 = \\cfrac{3}{-3} = -1\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"111\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0418\u0437 \u0432\u0442\u043e\u0440\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0441\u0438\u0441\u0442\u0435\u043c\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2789190f1df15f5bd570b643d9bb29f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_2:\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"26\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-45078dcd57cac62db8e98338a22dd939_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3a_2=6\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"59\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0580c5be6b3c77cbd727adef2f128343_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_2=\\cfrac{6}{3} = 2\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"83\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0418, \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u0438\u0437 \u043f\u0435\u0440\u0432\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0441\u0438\u0441\u0442\u0435\u043c\u044b \u0448\u0430\u0433\u043e\u0432 \u043d\u0430\u0445\u043e\u0434\u0438\u043c \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u0443\u044e <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c80696de686104689a20cb70c0033830_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1:\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"26\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1db29b41da87b5381698bd496ad4887e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1 +a_2-a_3 = 4 \\ \\xrightarrow{a_3\\ = \\ -1 \\ ; \\ a_2 \\ = \\ 2 } \\ a_1 +2-(-1) = 4\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"411\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b02c7b15b3b51ac99fe4d36f6f084283_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1 = 4-2-1\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"110\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d561c23489e6cc9b0680dbe0601babbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1 = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"49\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u0441\u0438\u0441\u0442\u0435\u043c\u044b \u043b\u0438\u043d\u0435\u0439\u043d\u044b\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u0438\u043c\u0435\u0435\u0442 \u0432\u0438\u0434:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a770689380f00a654857e19b755a1dd6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1=1 \\qquad a_2=2 \\qquad a_3 = -1\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"233\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0418\u0442\u0430\u043a, \u0432\u0435\u043a\u0442\u043e\u0440<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-88e41d561c3898029b7b94d7014c1e79_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0415\u0433\u043e \u043c\u043e\u0436\u043d\u043e \u0432\u044b\u0440\u0430\u0437\u0438\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u0435\u0439: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-80aba06b670bf9eedd4074be0750c3d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{x}}= a_1\\vv{\\text{u}}+a_2\\vv{\\text{v}}+ a_3\\vv{\\text{w}}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"160\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7115a844fd089e1dd6d17e0148dfe115_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{x}}= 1\\vv{\\text{u}}+2\\vv{\\text{v}}-1\\vv{\\text{w}}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"135\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5042840d8d9f0844c2f122aa96f850a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\mathbf{x}}\\bm{= }\\vv{\\mathbf{u}}\\bm{+} \\bm{2} \\vv{\\mathbf{v}} \\bm{-} \\vv{\\mathbf{w}}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"98\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 3<\/h3>\n<p> \u0412\u044b\u0440\u0430\u0437\u0438\u0442\u0435 \u0432\u0435\u043a\u0442\u043e\u0440<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-88e41d561c3898029b7b94d7014c1e79_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u043a\u0430\u043a \u043b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4b6be5a59bbf478047e4f3ace338ee48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}, \\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"27\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u0418 <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d8af8ced46d93e73dc5290e0cca4dc6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{w}}.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"17\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e87fcd25b965f26fff25c11b2c341f5e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{x}} = (-1,5,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"116\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f4d916d955d40ff456668de002eebc5e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (1,3,-1) \\qquad \\vv{\\text{v}} = (2,-3,-2) \\qquad \\vv{\\text{w}} = (0,-2,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"397\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u041c\u044b \u043f\u0440\u0435\u0434\u043b\u0430\u0433\u0430\u0435\u043c \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0435 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u043e\u043d\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u0430 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-910bbc90f3e6b9fb743fe6e64dbb83d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{x}} :\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"18\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-06d3d6ec5ca4921b109f8f974e73cbbd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1\\vv{\\text{u}}+a_2\\vv{\\text{v}}+ a_3\\vv{\\text{w}}=\\vv{\\text{x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"160\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u0437\u0430\u043c\u0435\u043d\u044f\u0435\u043c \u043a\u0430\u0436\u0434\u044b\u0439 \u0432\u0435\u043a\u0442\u043e\u0440 \u0435\u0433\u043e \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u0430\u043c\u0438:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6c8f5b0f83b3724f96bea45f4f8c6770_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1\\begin{pmatrix} 1 \\\\3\\\\-1 \\end{pmatrix}+a_2\\begin{pmatrix} 2 \\\\-3\\\\-2 \\end{pmatrix}+ a_3\\begin{pmatrix} 0 \\\\-2\\\\1 \\end{pmatrix}=\\begin{pmatrix} -1 \\\\5\\\\-3 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"64\" width=\"337\" style=\"vertical-align: -27px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041c\u044b \u0443\u043c\u043d\u043e\u0436\u0430\u0435\u043c \u043a\u0430\u0436\u0434\u044b\u0439 \u0432\u0435\u043a\u0442\u043e\u0440 \u043d\u0430 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044e\u0449\u0435\u0435 \u0435\u043c\u0443 \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e\u0435:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-66170c955f7d70bd675d864ad5f346a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix} a_1 \\\\3a_1\\\\-a_1 \\end{pmatrix}+\\begin{pmatrix} 2a_2 \\\\ -3a_2\\\\ -2a_2 \\end{pmatrix}+ \\begin{pmatrix} 0 \\\\-2a_3\\\\a_3 \\end{pmatrix}=\\begin{pmatrix} -1 \\\\5\\\\-3 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"64\" width=\"314\" style=\"vertical-align: -27px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041e\u0441\u0443\u0449\u0435\u0441\u0442\u0432\u043b\u044f\u0435\u043c \u0441\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e2a60cf7c088c8640c23e6c86ed1c00d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix} a_1 +2a_2\\\\3a_1-3a_2-2a_3\\\\ -a_1-2a_2+a_3 \\end{pmatrix}=\\begin{pmatrix} -1 \\\\5\\\\-3 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"64\" width=\"220\" style=\"vertical-align: -27px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u043b\u0438 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0443\u044e \u0441\u0438\u0441\u0442\u0435\u043c\u0443 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-acdcf13a945bca16684be340d27e3523_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{l} a_1 +2a_2 = -1 \\\\[2ex] 3a_1-3a_2-2a_3 =5\\\\[2ex] -a_1-2a_2+a_3 = -3 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"185\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0420\u0435\u0448\u0430\u0435\u043c \u0441\u0438\u0441\u0442\u0435\u043c\u0443, \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u0443\u044e \u043c\u0435\u0442\u043e\u0434\u043e\u043c \u0413\u0430\u0443\u0441\u0441\u0430: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e49ae26fc68a865214bd9b6146b7aa99_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} 1&amp;2&amp;0&amp; -1 \\\\[2ex] 3&amp;-3&amp;-2&amp;5\\\\[2ex] -1&amp;-2&amp;1&amp;-3 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"177\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e4c56b420242d0abe6f77b3ed1a60e54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(\\begin{array}{ccc|c} 1&amp;2&amp;0&amp; -1 \\\\[2ex] 3&amp;-3&amp;-2&amp;5\\\\[2ex] -1&amp;-2&amp;1&amp;-3 \\end{array} \\right) \\begin{array}{c} \\\\[2ex] \\xrightarrow{F_2-3F_1}\\\\[2ex] \\xrightarrow{F_3+F_1} \\end{array} \\left( \\begin{array}{ccc|c} 1&amp;2&amp;0&amp; -1 \\\\[2ex] 0&amp;-9&amp;-2&amp;8\\\\[2ex] 0&amp;0&amp;1&amp;-4\\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"431\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u0430\u044f \u0441\u0438\u0441\u0442\u0435\u043c\u0430 \u0448\u0430\u0433\u043e\u0432 \u0442\u0430\u043a\u043e\u0432\u0430:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-03461ed9ebda463d2f0a1bb6894657be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{r} a_1 +2a_2 = -1 \\\\[2ex] -9a_2-2a_3 =8\\\\[2ex] a_3 = -4 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"140\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0412\u0441\u0435, \u0447\u0442\u043e \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u0441\u0434\u0435\u043b\u0430\u0442\u044c \u0441\u0435\u0439\u0447\u0430\u0441, \u044d\u0442\u043e \u043f\u0440\u043e\u044f\u0441\u043d\u0438\u0442\u044c \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e\u0435 \u0438 \u043d\u0430\u0439\u0442\u0438 \u0435\u0433\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435. \u0418\u0442\u0430\u043a, \u0438\u0437 \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0435\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043d\u0430\u0445\u043e\u0434\u0438\u043c <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a5e5ed86162a9b0324b8f44dc16fcbce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_3:\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"26\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0abc9e623042fbe70cd55d4084945584_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_3 = -4\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"64\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0418\u0437 \u0432\u0442\u043e\u0440\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0441\u0438\u0441\u0442\u0435\u043c\u044b \u043d\u0430\u0445\u043e\u0434\u0438\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2789190f1df15f5bd570b643d9bb29f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_2:\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"26\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6bb0b04bcb9cce3edf56853f8b035b69_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-9a_2-2a_3 =8 \\ \\xrightarrow{a_3 \\ = \\ -4} \\ -9a_2-2\\cdot (-4) = 8\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"357\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c798313fd76263436ded44def0ac8ba5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-9a_2+8 = 8\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"102\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dc1521b27dddd5c037002d19dbe60aa6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-9a_2 = 8-8\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"102\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e08abc2b86a9f1cc85f4da3e70f35532_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-9a_2 = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"71\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4f389c942cdaca52620cd707a732d2d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_2=\\cfrac{0}{-9} = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"98\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0418 \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u0438\u0437 \u043f\u0435\u0440\u0432\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0441\u0438\u0441\u0442\u0435\u043c\u044b \u0448\u0430\u0433\u043e\u0432 \u0440\u0435\u0448\u0430\u0435\u043c \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e\u0435 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c80696de686104689a20cb70c0033830_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1:\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"26\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9a77d42eebe2f101d7b1e88fce265b36_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1 +2a_2 = -1 \\ \\xrightarrow{a_2 \\ = \\ 0 } \\ a_1=-1\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"249\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u0441\u0438\u0441\u0442\u0435\u043c\u044b \u043b\u0438\u043d\u0435\u0439\u043d\u044b\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u0438\u043c\u0435\u0435\u0442 \u0432\u0438\u0434:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d3d20ab34707d782258ff1df42a5a843_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1=-1 \\qquad a_2=0 \\qquad a_3 = -4\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"248\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0418\u0442\u0430\u043a, \u0432\u0435\u043a\u0442\u043e\u0440<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-88e41d561c3898029b7b94d7014c1e79_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u043e \u043f\u0443\u0442\u0435\u043c \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0433\u043e \u043e\u0431\u044a\u0435\u0434\u0438\u043d\u0435\u043d\u0438\u044f \u0434\u0440\u0443\u0433\u0438\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-80aba06b670bf9eedd4074be0750c3d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{x}}= a_1\\vv{\\text{u}}+a_2\\vv{\\text{v}}+ a_3\\vv{\\text{w}}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"160\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c008e155198c2dd0d0e6beadda92f677_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{x}}= -1\\vv{\\text{u}}+0\\vv{\\text{v}}-4\\vv{\\text{w}}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"149\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8327b18d65318a6d15255b12ac67aa82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\mathbf{x}}\\bm{= -}\\vv{\\mathbf{u}}\\bm{-4} \\vv{\\mathbf{w}}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"92\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 4<\/h3>\n<p> \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043b\u0438 \u0432\u0435\u043a\u0442\u043e\u0440<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-88e41d561c3898029b7b94d7014c1e79_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u043c\u043e\u0436\u043d\u043e \u0432\u044b\u0440\u0430\u0437\u0438\u0442\u044c \u043a\u0430\u043a \u043b\u0438\u043d\u0435\u0439\u043d\u0443\u044e \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044e \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4b6be5a59bbf478047e4f3ace338ee48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}, \\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"27\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u0418<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d8af8ced46d93e73dc5290e0cca4dc6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{w}}.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"17\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0412 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u043d\u0430\u0439\u0434\u0438\u0442\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u0438\u0445 \u0441\u0432\u044f\u0437\u044b\u0432\u0430\u0435\u0442. <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-39c6f0a533d9bb15483b3ee9bbd2b1cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{x}} = (2,1,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"102\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e03e61028e9e49d640d0702e0ee056e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (3,-1,1) \\qquad \\vv{\\text{v}} = (-1,2,0) \\qquad \\vv{\\text{w}} = (1,3,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"369\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u0422\u0430\u043a \u0447\u0442\u043e \u0432\u0435\u043a\u0442\u043e\u0440<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-88e41d561c3898029b7b94d7014c1e79_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0431\u044b\u0442\u044c \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u0435\u0439 \u0434\u0440\u0443\u0433\u0438\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432, \u0434\u043e\u043b\u0436\u043d\u043e \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0442\u044c\u0441\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-06d3d6ec5ca4921b109f8f974e73cbbd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1\\vv{\\text{u}}+a_2\\vv{\\text{v}}+ a_3\\vv{\\text{w}}=\\vv{\\text{x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"160\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u0437\u0430\u043c\u0435\u043d\u044f\u0435\u043c \u043a\u0430\u0436\u0434\u044b\u0439 \u0432\u0435\u043a\u0442\u043e\u0440 \u0435\u0433\u043e \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0430\u043c\u0438:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-649abb0a558488a33e4f1e89d952dbf4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1\\begin{pmatrix} 3 \\\\-1\\\\1 \\end{pmatrix}+a_2\\begin{pmatrix} -1 \\\\2\\\\0 \\end{pmatrix}+ a_3\\begin{pmatrix} 1 \\\\3\\\\1 \\end{pmatrix}=\\begin{pmatrix} 2 \\\\1\\\\-1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"64\" width=\"323\" style=\"vertical-align: -27px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0423\u043c\u043d\u043e\u0436\u0430\u0435\u043c \u043a\u0430\u0436\u0434\u044b\u0439 \u0432\u0435\u043a\u0442\u043e\u0440 \u043d\u0430 \u0435\u0433\u043e \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e555b6f0b4b201e2678bd843d6924f0b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix} 3a_1 \\\\-a_1\\\\a_1 \\end{pmatrix}+\\begin{pmatrix} -a_2 \\\\2a_2\\\\0 \\end{pmatrix}+ \\begin{pmatrix} a_3 \\\\3a_3\\\\a_3 \\end{pmatrix}=\\begin{pmatrix} 2 \\\\1\\\\-1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"64\" width=\"292\" style=\"vertical-align: -27px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0414\u043e\u0431\u0430\u0432\u043b\u044f\u0435\u043c \u0432\u0435\u043a\u0442\u043e\u0440\u044b:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c3437e5ddbc157f4471e2a6524f0f5ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix} 3a_1 -a_2+a_3\\\\-a_1+2a_2+3a_3\\\\ a_1+a_3 \\end{pmatrix}=\\begin{pmatrix} 2 \\\\1\\\\-1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"64\" width=\"225\" style=\"vertical-align: -27px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u043d\u043e \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0441\u0438\u0441\u0442\u0435\u043c\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f51b7e801b8314c51b983f1f24be15e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{l} 3a_1 -a_2+a_3 = 2 \\\\[2ex] -a_1+2a_2+3a_3 =1\\\\[2ex] a_1+a_3 = -1 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"180\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0420\u0435\u0448\u0438\u043c \u0442\u0435\u043f\u0435\u0440\u044c \u0441\u0438\u0441\u0442\u0435\u043c\u0443, \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u0443\u044e \u043c\u0435\u0442\u043e\u0434\u043e\u043c \u0413\u0430\u0443\u0441\u0441\u0430: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-031b14d5aca6a41d897ca575440b1197_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} 3&amp;-1&amp;1&amp; 2 \\\\[2ex] -1&amp;2&amp;3&amp;1\\\\[2ex] 1&amp;0&amp;1&amp;-1 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"163\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2caf1e1104b8b67e13d452bbd20d13b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(\\begin{array}{ccc|c} 3&amp;-1&amp;1&amp; 2 \\\\[2ex] -1&amp;2&amp;3&amp;1\\\\[2ex] 1&amp;0&amp;1&amp;-1 \\end{array} \\right) \\begin{array}{c} \\\\[2ex] \\xrightarrow{3F_2+F_1}\\\\[2ex] \\xrightarrow{3F_3-F_1} \\end{array} \\left( \\begin{array}{ccc|c} 3&amp;-1&amp;1&amp; 2 \\\\[2ex] 0&amp;5&amp;10&amp;5\\\\[2ex] 0&amp;1&amp;2&amp;-5\\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"412\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d4deec2426c0b9bb0b8e8a3d95155fd9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(\\begin{array}{ccc|c} 3&amp;-1&amp;1&amp; 2 \\\\[2ex] 0&amp;5&amp;10&amp;5\\\\[2ex] 0&amp;1&amp;2&amp;-5 \\end{array} \\right) \\begin{array}{c} \\\\[2ex] \\\\[2ex] \\xrightarrow{5F_3-F_2} \\end{array} \\left( \\begin{array}{ccc|c}3&amp;-1&amp;1&amp; 2 \\\\[2ex] 0&amp;5&amp;10&amp;5\\\\[2ex] 0&amp;0&amp;0&amp;-30\\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"416\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u043b\u0438 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0443\u044e \u0441\u0438\u0441\u0442\u0435\u043c\u0443 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e537d5c481ceedeaebf95334d72199ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{r} 3a_1 -a_2+a_3 = 2 \\\\[2ex] 5a_2 +10a_3=5\\\\[2ex] 0 = -30 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"157\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041e\u0434\u043d\u0430\u043a\u043e \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0435\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043d\u0438\u043a\u043e\u0433\u0434\u0430 \u043d\u0435 \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u0432\u044b\u043f\u043e\u043b\u043d\u0435\u043d\u043e, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 0 \u043d\u0438\u043a\u043e\u0433\u0434\u0430 \u043d\u0435 \u0431\u0443\u0434\u0435\u0442 \u0440\u0430\u0432\u0435\u043d -30, \u043a\u0430\u043a\u0438\u0435 \u0431\u044b \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u043d\u0438 \u043f\u0440\u0438\u043d\u0438\u043c\u0430\u043b\u0438 \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u0435. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0441\u0438\u0441\u0442\u0435\u043c\u0430 \u043d\u0435 \u0438\u043c\u0435\u0435\u0442 \u0440\u0435\u0448\u0435\u043d\u0438\u044f, \u0430 \u044d\u0442\u043e \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e <strong>\u043d\u0435 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u0438<\/strong> \u0434\u043b\u044f \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u0430<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9f9ba5824d0d2c7ebfa020ea72dc6a11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{x}}.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u041d\u0430 \u044d\u0442\u043e\u0439 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0435 \u0432\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u043e\u0431\u044a\u044f\u0441\u043d\u0435\u043d\u0438\u0435 \u0442\u043e\u0433\u043e, \u0447\u0442\u043e \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442 \u043b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u043f\u0440\u0438\u043c\u0435\u0440 \u0442\u043e\u0433\u043e, \u043a\u0430\u043a \u0432\u0435\u043a\u0442\u043e\u0440 \u0432\u044b\u0440\u0430\u0436\u0430\u0435\u0442\u0441\u044f \u0432 \u0432\u0438\u0434\u0435 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u0438, \u0438, \u043a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u043f\u043e\u043f\u0440\u0430\u043a\u0442\u0438\u043a\u043e\u0432\u0430\u0442\u044c\u0441\u044f \u0441 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f\u043c\u0438 \u0438 \u0437\u0430\u0434\u0430\u0447\u0430\u043c\u0438, \u0440\u0435\u0448\u0430\u0435\u043c\u044b\u043c\u0438 \u0448\u0430\u0433 \u0437\u0430 \u0448\u0430\u0433\u043e\u043c. \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432? \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u0438 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435: \u041b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044f \u043d\u0430\u0431\u043e\u0440\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u2014 \u044d\u0442\u043e &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ru\/%d0%bf%d1%80%d0%b8%d0%bc%d0%b5%d1%80%d1%8b-%d0%bb%d0%b8%d0%bd%d0%b5%d0%b8%d0%bd%d0%be%d0%b8-%d0%ba%d0%be%d0%bc%d0%b1%d0%b8%d0%bd%d0%b0%d1%86%d0%b8%d0%b8-%d0%b2%d0%b5%d0%ba%d1%82%d0%be%d1%80%d0%be\/\"> <span class=\"screen-reader-text\">\u041b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432<\/span> \u0427\u0438\u0442\u0430\u0442\u044c \u0434\u0430\u043b\u0435\u0435 &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[22],"tags":[],"class_list":["post-73","post","type-post","status-publish","format-standard","hentry","category-22"],"yoast_head":"<!-- This site is optimized 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\u043d\u0430\u0431\u043e\u0440\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u2014 \u044d\u0442\u043e &hellip; \u041b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u0427\u0438\u0442\u0430\u0442\u044c \u0434\u0430\u043b\u0435\u0435 &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/ru\/\u043f\u0440\u0438\u043c\u0435\u0440\u044b-\u043b\u0438\u043d\u0435\u0438\u043d\u043e\u0438-\u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u0438-\u0432\u0435\u043a\u0442\u043e\u0440\u043e\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-09-16T13:04:23+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-33729e6d20b00643b5d9ddf38544c11c_l3.png\" \/>\n<meta name=\"author\" content=\"Mathority \u041a\u043e\u043c\u0430\u043d\u0434\u0430\" \/>\n<meta name=\"twitter:card\" 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