{"id":72,"date":"2023-09-16T13:05:25","date_gmt":"2023-09-16T13:05:25","guid":{"rendered":"https:\/\/mathority.org\/ru\/%d0%bd%d0%b5%d0%b7%d0%b0%d0%b2%d0%b8%d1%81%d0%b8%d0%bc%d1%8b%d0%b5-%d0%b8-%d0%bb%d0%b8%d0%bd%d0%b5%d0%b8%d0%bd%d0%be-%d0%b7%d0%b0%d0%b2%d0%b8%d1%81%d0%b8%d0%bc%d1%8b%d0%b5-%d0%b2%d0%b5%d0%ba%d1%82\/"},"modified":"2023-09-16T13:05:25","modified_gmt":"2023-09-16T13:05:25","slug":"%d0%bd%d0%b5%d0%b7%d0%b0%d0%b2%d0%b8%d1%81%d0%b8%d0%bc%d1%8b%d0%b5-%d0%b8-%d0%bb%d0%b8%d0%bd%d0%b5%d0%b8%d0%bd%d0%be-%d0%b7%d0%b0%d0%b2%d0%b8%d1%81%d0%b8%d0%bc%d1%8b%d0%b5-%d0%b2%d0%b5%d0%ba%d1%82","status":"publish","type":"post","link":"https:\/\/mathority.org\/ru\/%d0%bd%d0%b5%d0%b7%d0%b0%d0%b2%d0%b8%d1%81%d0%b8%d0%bc%d1%8b%d0%b5-%d0%b8-%d0%bb%d0%b8%d0%bd%d0%b5%d0%b8%d0%bd%d0%be-%d0%b7%d0%b0%d0%b2%d0%b8%d1%81%d0%b8%d0%bc%d1%8b%d0%b5-%d0%b2%d0%b5%d0%ba%d1%82\/","title":{"rendered":"\u041b\u0438\u043d\u0435\u0439\u043d\u043e \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u0435 \u0438 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u044b (\u043b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u0438 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c)"},"content":{"rendered":"<p>\u041d\u0430 \u044d\u0442\u043e\u0439 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0435 \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u044f\u0435\u043c, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u0435 \u0438 \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u044b. \u0412\u044b \u0442\u0430\u043a\u0436\u0435 \u0443\u0432\u0438\u0434\u0438\u0442\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u0442\u043e\u0433\u043e, \u043a\u0430\u043a \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043b\u0438 \u043d\u0430\u0431\u043e\u0440 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u043c \u0438\u043b\u0438 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u043c. \u0410, \u043a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u043f\u043e\u0448\u0430\u0433\u043e\u0432\u044b\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f \u0438 \u0440\u0435\u0448\u0430\u0435\u043c\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u043d\u0430 \u043b\u0438\u043d\u0435\u0439\u043d\u0443\u044e \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u0438 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c. <\/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-son-los-vectores-linealmente-independientes\"><\/span> \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u044b? <span class=\"ez-toc-section-end\"><\/span><\/h2>\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\"> \u041c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u043e \u0441\u0432\u043e\u0431\u043e\u0434\u043d\u044b\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f <strong>\u043b\u0438\u043d\u0435\u0439\u043d\u043e \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u043c,<\/strong> \u0435\u0441\u043b\u0438 \u043d\u0438 \u043e\u0434\u0438\u043d \u0438\u0437 \u043d\u0438\u0445 \u043d\u0435 \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u0437\u0430\u043f\u0438\u0441\u0430\u043d \u0432 \u0432\u0438\u0434\u0435 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u0438 \u0434\u0440\u0443\u0433\u0438\u0445.<\/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> \u041e\u043d\u0438 \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b, \u0435\u0441\u043b\u0438 \u0435\u0434\u0438\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0433\u043e \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-300ebfc809f336b8eba997c6d2b17b0b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1\\vv{\\text{v}}_1+a_2\\vv{\\text{v}}_2+\\dots + a_n\\vv{\\text{v}}_n=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"224\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\"> \u042d\u0442\u043e \u0432\u0441\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> \u0440\u0430\u0432\u043d\u043e 0: <\/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-343093bdf0637093707400807a880327_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1=a_2=\\dots = a_n=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"177\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-105\"><\/div>\n<\/div>\n<p> \u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438 \u0434\u0432\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b, \u0435\u0441\u043b\u0438 \u043e\u043d\u0438 \u043d\u0435 \u0438\u043c\u0435\u044e\u0442 \u043e\u0434\u043d\u043e\u0433\u043e \u0438 \u0442\u043e\u0433\u043e \u0436\u0435 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u044f, \u0442\u043e \u0435\u0441\u0442\u044c \u0435\u0441\u043b\u0438 \u043e\u043d\u0438 \u043d\u0435 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b.<\/p>\n<p> \u0414\u043b\u044f \u043a\u0440\u0430\u0442\u043a\u043e\u0441\u0442\u0438 \u0438\u043d\u043e\u0433\u0434\u0430 \u043f\u0440\u044f\u043c\u043e \u0433\u043e\u0432\u043e\u0440\u0438\u043c, \u0447\u0442\u043e \u044d\u0442\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u044b LI. \u0418\u043b\u0438 \u0447\u0442\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u044b \u043e\u0431\u043b\u0430\u0434\u0430\u044e\u0442 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c\u044e. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-son-los-vectores-linealmente-dependientes\"><\/span> \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u044b?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041e\u0447\u0435\u0432\u0438\u0434\u043d\u043e, \u0447\u0442\u043e \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u044b \u043e\u0437\u043d\u0430\u0447\u0430\u044e\u0442 \u043f\u0440\u043e\u0442\u0438\u0432\u043e\u043f\u043e\u043b\u043e\u0436\u043d\u043e\u0441\u0442\u044c \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u043c \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u0435\u0433\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0442\u0430\u043a\u043e\u0432\u043e: <\/p>\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\"> \u041c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u043e \u0441\u0432\u043e\u0431\u043e\u0434\u043d\u044b\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 <strong>\u043b\u0438\u043d\u0435\u0439\u043d\u043e \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e,<\/strong> \u0435\u0441\u043b\u0438 \u043b\u044e\u0431\u043e\u0439 \u0438\u0437 \u043d\u0438\u0445 \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 \u0434\u0440\u0443\u0433\u0438\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432, \u043e\u0431\u0440\u0430\u0437\u0443\u044e\u0449\u0438\u0445 \u0441\u0438\u0441\u0442\u0435\u043c\u0443.<\/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> \u041e\u043d\u0438 \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b, \u0435\u0441\u043b\u0438 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0433\u043e \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-300ebfc809f336b8eba997c6d2b17b0b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1\\vv{\\text{v}}_1+a_2\\vv{\\text{v}}_2+\\dots + a_n\\vv{\\text{v}}_n=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"224\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\"> \u0432 \u043a\u043e\u0442\u043e\u0440\u043e\u043c \u0438\u043c\u0435\u0435\u0442 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u044b\u0439 \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-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> \u043e\u0442\u043b\u0438\u0447\u0430\u0435\u0442\u0441\u044f \u043e\u0442 0: <\/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-439f0ac04db138f5e47e7ffa3010ac82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_i\\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"48\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-106\"><\/div>\n<\/div>\n<p> \u0412\u0435\u0440\u043d\u043e \u0438 \u043e\u0431\u0440\u0430\u0442\u043d\u043e\u0435: \u0435\u0441\u043b\u0438 \u0432\u0435\u043a\u0442\u043e\u0440 \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\u0440\u0443\u0433\u0438\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432, \u0442\u043e \u0432\u0441\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u044b \u0432 \u043d\u0430\u0431\u043e\u0440\u0435 \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b.<\/p>\n<p> \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0435\u0441\u043b\u0438 \u0434\u0432\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b, \u044d\u0442\u043e \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e \u043e\u043d\u0438 \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b.<\/p>\n<p> \u0418\u043d\u043e\u0433\u0434\u0430 \u0438\u0445 \u0442\u0430\u043a\u0436\u0435 \u0441\u043e\u043a\u0440\u0430\u0449\u0430\u044e\u0442 \u0438 \u043d\u0430\u0437\u044b\u0432\u0430\u044e\u0442 \u043f\u0440\u043e\u0441\u0442\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c\u0438 LD. \u0418\u043b\u0438 \u0434\u0430\u0436\u0435 \u0447\u0442\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u044b \u0438\u043c\u0435\u044e\u0442 \u043b\u0438\u043d\u0435\u0439\u043d\u0443\u044e \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-saber-si-los-vectores-son-linealmente-dependientes-o-independientes\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440 \u0442\u043e\u0433\u043e, \u043a\u0430\u043a \u0443\u0437\u043d\u0430\u0442\u044c, \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u043b\u0438 \u0432\u0435\u043a\u0442\u043e\u0440\u044b \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<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0417\u0430\u0442\u0435\u043c \u043c\u044b \u0443\u0432\u0438\u0434\u0438\u043c \u0442\u0438\u043f\u0438\u0447\u043d\u044b\u0439 \u043f\u0440\u0438\u043c\u0435\u0440 \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.<\/p>\n<ul>\n<li> \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435, \u0438\u043c\u0435\u044e\u0442 \u043b\u0438 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 3 \u0442\u0440\u0435\u0445\u043c\u0435\u0440\u043d\u044b\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043b\u0438\u043d\u0435\u0439\u043d\u0443\u044e \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u0438\u043b\u0438 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c:<\/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-05af06eeddc930d2a2a1aef3557f1804_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (1,5,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"89\" 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-8499337b8d833980eb798442df144157_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}} = (-2,3,-1)\" 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-cfab263ab4dab31ac33ce94bf5cd605a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{w}} = (4,2,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"92\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u0412\u043e-\u043f\u0435\u0440\u0432\u044b\u0445, \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u0441\u0444\u043e\u0440\u043c\u0443\u043b\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u0443\u0441\u043b\u043e\u0432\u0438\u0435 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\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-2580c2225e7e01a88d80c323da49b776_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}}=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"159\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p> \u0422\u0435\u043f\u0435\u0440\u044c \u0437\u0430\u043c\u0435\u043d\u0438\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. \u041a\u0430\u043a \u043d\u043e\u043b\u044c, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u0435\u0442 \u043d\u0443\u043b\u0435\u0432\u043e\u043c\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\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-7b93accc41aaa4124dbe17d48b613380_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1(1,5,2)+a_2(-2,3,-1)+ a_3(4,2,1)=(0,0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"370\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b \u0443\u043c\u043d\u043e\u0436\u0430\u044e\u0442 \u0432\u0435\u043a\u0442\u043e\u0440\u044b, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u043d\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-e862c54b435070e58979525edbd3982b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a_1,5a_1,2a_1)+(-2a_2,3a_2,-a_2) + (4a_3,2a_3,a_3)=(0,0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"444\" style=\"vertical-align: -5px;\"><\/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-aeeebd2fc4c71c53bb5b69a7ba4712fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a_1-2a_2+4a_3 \\ , \\ 5a_1+3a_2+2a_3 \\ , \\ 2a_1-a_2+a_3)=(0,0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"468\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0415\u0441\u043b\u0438 \u043f\u0440\u0438\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c\u0441\u044f, \u0442\u043e \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u043c\u0443 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044e \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044e\u0442 3 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f, \u0442\u0430\u043a \u043a\u0430\u043a \u043a\u0430\u0436\u0434\u0430\u044f \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0430 \u043b\u0435\u0432\u043e\u0433\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u0434\u043e\u043b\u0436\u043d\u0430 \u0431\u044b\u0442\u044c \u0440\u0430\u0432\u043d\u0430 \u043a\u0430\u0436\u0434\u043e\u0439 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0435 \u043f\u0440\u0430\u0432\u043e\u0433\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u0430. \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043c\u044b \u0438\u043c\u0435\u0435\u043c \u043e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u0443\u044e \u0441\u0438\u0441\u0442\u0435\u043c\u0443 \u0438\u0437 \u0442\u0440\u0435\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u0441 \u0442\u0440\u0435\u043c\u044f \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\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-c6bb8117dd8ae715314efe73fe65eed8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{l} a_1-2a_2+4a_3 = 0 \\\\[2ex] 5a_1+3a_2+2a_3 =0\\\\[2ex] 2a_1-a_2+a_3 = 0 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"175\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u0435\u0434\u0438\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0435, \u0447\u0442\u043e \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u0441\u0434\u0435\u043b\u0430\u0442\u044c, \u044d\u0442\u043e \u0440\u0435\u0448\u0438\u0442\u044c \u0441\u0438\u0441\u0442\u0435\u043c\u0443 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439, \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u0435 \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u0440\u0430\u0432\u043d\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-5eff362725f9c8095e12f173e039328e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_3.\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"21\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u043c\u043e\u0436\u043d\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u043b\u044e\u0431\u043e\u0439 \u043c\u0435\u0442\u043e\u0434 (\u043c\u0435\u0442\u043e\u0434 \u0437\u0430\u043c\u0435\u043d\u044b, \u043c\u0435\u0442\u043e\u0434 \u0413\u0430\u0443\u0441\u0430, \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u041a\u0440\u0430\u043c\u0435\u0440\u0430 \u0438 \u0442. \u0434.). \u041e\u0434\u043d\u0430\u043a\u043e, \u0447\u0442\u043e\u0431\u044b \u0443\u0437\u043d\u0430\u0442\u044c, \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u043b\u0438 \u0432\u0435\u043a\u0442\u043e\u0440\u044b LI \u0438\u043b\u0438 LD, \u0434\u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c, \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u043b\u0438 \u0440\u0435\u0448\u0435\u043d\u0438\u0435, \u043e\u0442\u043b\u0438\u0447\u043d\u043e\u0435 \u043e\u0442 \u0442\u0440\u0438\u0432\u0438\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u044f (\u0432\u0441\u0435 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b \u0440\u0430\u0432\u043d\u044b \u043d\u0443\u043b\u044e). \u0422\u0410\u041a: <\/p>\n<div style=\"background-color:#FFCC8080;padding-top: 20px; padding-bottom: 0.5px; padding-right: 40px; padding-left: 12px; border: 2px solid #FFB74D; border-radius:20px;\">\n<ul>\n<li style=\"margin-bottom:24px\"> \u0415\u0441\u043b\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u043c\u0430\u0442\u0440\u0438\u0446\u044b, \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u043d\u043e\u0439 \u0438\u0437 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432, \u043e\u0442\u043b\u0438\u0447\u0435\u043d \u043e\u0442 \u043d\u0443\u043b\u044f, \u044d\u0442\u043e \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e \u0441\u0438\u0441\u0442\u0435\u043c\u0430 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u0438\u043c\u0435\u0435\u0442 \u0442\u043e\u043b\u044c\u043a\u043e \u043e\u0434\u043d\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u0435 (\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-485cb2ce7f28253bda0a1262eeec81b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1=a_2=a_3=\\dots=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"175\" style=\"vertical-align: -3px;\"><\/p>\n<p> ) \u0438, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0432\u0435\u043a\u0442\u043e\u0440\u044b <strong>\u043b\u0438\u043d\u0435\u0439\u043d\u043e \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b<\/strong><\/li>\n<li style=\"margin-bottom:14px\"> \u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u0435\u0441\u043b\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u043c\u0430\u0442\u0440\u0438\u0446\u044b, \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u043d\u043e\u0439 \u0438\u0437 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432, \u0440\u0430\u0432\u0435\u043d \u043d\u0443\u043b\u044e, \u044d\u0442\u043e \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e \u0441\u0438\u0441\u0442\u0435\u043c\u0430 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u0438\u043c\u0435\u0435\u0442 \u0431\u043e\u043b\u0435\u0435 \u043e\u0434\u043d\u043e\u0433\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0438, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0432\u0435\u043a\u0442\u043e\u0440\u044b <strong>\u043b\u0438\u043d\u0435\u0439\u043d\u043e \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b<\/strong> .<\/li>\n<\/ul>\n<\/div>\n<p> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0435\u0434\u0438\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0435, \u0447\u0442\u043e \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c, \u2014 \u044d\u0442\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u0441 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0430\u043c\u0438 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 (\u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u044d\u0442\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c 3&#215;3, \u0435\u0433\u043e \u043c\u043e\u0436\u043d\u043e \u0440\u0435\u0448\u0438\u0442\u044c \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043f\u0440\u0430\u0432\u0438\u043b\u0430 \u0421\u0430\u0440\u0440\u0443\u0441\u0430). \u042d\u0442\u043e\u0442 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u0435\u0442 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u0430\u043c \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u0439 \u0441\u0438\u0441\u0442\u0435\u043c\u044b \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-046e05ff603822985510c7bdc8b73021_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} 1&amp;-2&amp;4\\\\[1.1ex] 5&amp;3&amp;2 \\\\[1.1ex] 2&amp;-1&amp;1 \\end{vmatrix} = -37 \\bm{\\neq 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"165\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0412 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u043e\u0442\u043b\u0438\u0447\u0435\u043d \u043e\u0442 0, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u044b <strong>\u043b\u0438\u043d\u0435\u0439\u043d\u043e \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b<\/strong> .<\/p>\n<p> \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u0435\u0434\u0438\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u043c \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u044b\u043c \u0440\u0435\u0448\u0435\u043d\u0438\u0435\u043c \u0441\u0438\u0441\u0442\u0435\u043c\u044b \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0442\u0440\u0438\u0432\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u0441\u043e \u0432\u0441\u0435\u043c\u0438 \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u043c\u0438, \u0440\u0430\u0432\u043d\u044b\u043c\u0438 \u043d\u0443\u043b\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-55102cbf302a51cdb904a4f3ad88e658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1=a_2=a_3=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"131\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-de-los-vectores-linealmente-dependientes-e-independientes\"><\/span> \u0421\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \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 <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> \u041b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u0438\u043b\u0438 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u0438\u043c\u0435\u0435\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043a\u0438:<\/p>\n<ul>\n<li> \u0414\u0432\u0430 \u043f\u0440\u043e\u043f\u043e\u0440\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b \u0438, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0438\u043c\u0435\u044e\u0442 \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u043e\u0435 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435.<\/li>\n<\/ul>\n<ul>\n<li> \u0410\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u043e, \u0435\u0441\u043b\u0438 \u0434\u0432\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043d\u0435 \u0438\u043c\u0435\u044e\u0442 \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u043e\u0433\u043e \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u044f \u0438\u043b\u0438 \u043d\u0435\u043f\u0440\u043e\u043f\u043e\u0440\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b, \u043e\u043d\u0438 \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b.<\/li>\n<\/ul>\n<ul>\n<li> \u0422\u0440\u0438 \u043a\u043e\u043c\u043f\u043b\u0430\u043d\u0430\u0440\u043d\u044b\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 (\u043d\u0430\u0445\u043e\u0434\u044f\u0449\u0438\u0435\u0441\u044f \u0432 \u043e\u0434\u043d\u043e\u0439 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438) \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b.<\/li>\n<\/ul>\n<ul>\n<li> \u041d\u0443\u043b\u0435\u0432\u043e\u0439 \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-40f8606fdc9522ef08a3d4b889a3d840_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\vv{\\text{v}}=(0,0,0))\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"101\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u043e\u0442 \u043b\u044e\u0431\u043e\u0433\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u0430.<\/li>\n<\/ul>\n<ul>\n<li> \u041d\u0430\u0431\u043e\u0440 \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u043f\u043e\u0440\u043e\u0436\u0434\u0430\u0435\u0442 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u043e \u0438 \u043e\u0431\u0440\u0430\u0437\u0443\u0435\u0442 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u044b\u0439 \u0431\u0430\u0437\u0438\u0441. \u0415\u0441\u043b\u0438 \u0442\u0440\u0438 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b, \u044d\u0442\u043e \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u0430\u044f \u0431\u0430\u0437\u0430. \u0410 \u0435\u0441\u043b\u0438 \u0435\u0433\u043e \u043c\u043e\u0434\u0443\u043b\u044c \u0442\u0430\u043a\u0436\u0435 \u0440\u0430\u0432\u0435\u043d 1, \u044d\u0442\u043e \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u0435\u0442 \u043e\u0440\u0442\u043e\u043d\u043e\u0440\u043c\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u043c\u0443 \u0431\u0430\u0437\u0438\u0441\u0443. <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-dependencia-e-independencia-lineal\"><\/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 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u0438 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041d\u0438\u0436\u0435 \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u043f\u043e\u043f\u0440\u0430\u043a\u0442\u0438\u043a\u043e\u0432\u0430\u0442\u044c\u0441\u044f \u0432 \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u0438\u0445 \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0445 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f\u0445 \u0441 \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u043c\u0438 \u0438 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u043c\u0438 \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c\u0438.<\/p>\n<h3 class=\"wp-block-heading\"> \u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 1<\/h3>\n<p> \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435, \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u043b\u0438 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u044b \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: <\/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-d552b4aa1666be818679ed4557aa7950_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (1,-2,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"103\" 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-044b61524cd81ac5ea271deaf60ba56f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}} = (2,1,3)\" 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-5f2e178b7cbb93d5b58a5a9d493b3e5b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{w}} = (5,-1,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"106\" 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\"> \u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u0441\u0444\u043e\u0440\u043c\u0443\u043b\u0438\u0440\u0443\u0435\u043c \u0443\u0441\u043b\u043e\u0432\u0438\u0435 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\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-2580c2225e7e01a88d80c323da49b776_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}}=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"159\" 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-62dca064bc122d1180bd344cc63b09ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1(1,-2,1)+a_2(2,1,3)+ a_3(5,-1,1)=(0,0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"370\" 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-358964cb9ab1a6719cd7fac6d80f35bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a_1,-2a_1,a_1)+(2a_2,a_2,3a_2) + (5a_3,-a_3,a_3)=(0,0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"427\" 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-4a60f9dd00a04a5d988a9d664befa3fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a_1+2a_2+5a_3 \\ , \\ -2a_1+a_2-a_3 \\ , \\ a_1+3a_2+a_3)=(0,0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"464\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u043c\u0443 \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0443 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u0435\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0430\u044f \u0441\u0438\u0441\u0442\u0435\u043c\u0430 \u043b\u0438\u043d\u0435\u0439\u043d\u044b\u0445 \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-58f1b449f48096570437df0ca40f8a8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{l} a_1+2a_2+5a_3 = 0 \\\\[2ex] -2a_1+a_2-a_3 =0\\\\[2ex] a_1+3a_2+a_3 = 0 \\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\"> \u041f\u043e\u0441\u043b\u0435 \u0442\u043e\u0433\u043e, \u043a\u0430\u043a \u043c\u044b \u0441\u0444\u043e\u0440\u043c\u0443\u043b\u0438\u0440\u043e\u0432\u0430\u043b\u0438 \u0441\u0438\u0441\u0442\u0435\u043c\u0443 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439, \u043c\u044b \u0440\u0435\u0448\u0430\u0435\u043c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0441 \u0435\u0435 \u0447\u043b\u0435\u043d\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-caa6d4f135e79bb8b6d2368ff7eebefb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} 1&amp;2&amp;5\\\\[1.1ex] -2&amp;1&amp;-1 \\\\[1.1ex] 1&amp;3&amp;1 \\end{vmatrix} = -29 \\bm{\\neq 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"179\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0412 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u043e\u0442\u043b\u0438\u0447\u0435\u043d \u043e\u0442 0, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0442\u0440\u0438 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 <strong>\u043b\u0438\u043d\u0435\u0439\u043d\u043e \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b<\/strong> \u0434\u0440\u0443\u0433 \u043e\u0442 \u0434\u0440\u0443\u0433\u0430.<\/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> \u041a\u043b\u0430\u0441\u0441\u0438\u0444\u0438\u0446\u0438\u0440\u0443\u0439\u0442\u0435 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u044b \u043a\u0430\u043a \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u0435 \u0438\u043b\u0438 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\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-4cc2ed855100fa8f5ef4d5a58eec547c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (1,4,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"89\" 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-1511660305e564364f81511fbcab382a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}} = (-2,0,2)\" 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-82f0ad7c365ea32003750cc4b55e44f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{w}} = (3,-1,-4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"120\" 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\"> \u041f\u0440\u0435\u0436\u0434\u0435 \u0432\u0441\u0435\u0433\u043e \u0441\u0444\u043e\u0440\u043c\u0443\u043b\u0438\u0440\u0443\u0435\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\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-2580c2225e7e01a88d80c323da49b776_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}}=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"159\" 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-28ebfd8d5f95694329a88caf6213a263_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1(1,4,3)+a_2(-2,0,2)+ a_3(3,-1,-4)=(0,0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"383\" 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-9e75b345f90c95164ef95890f9fd67ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a_1,4a_1,3a_1)+(-2a_2,0,2a_2) + (3a_3,-a_3,-4a_3)=(0,0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"450\" 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-221296d40e44e447a90dcdbb00752663_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a_1-2a_2+3a_3 \\ , \\ 4a_1-a_3 \\ , \\ 3a_1+2a_2-4a_3)=(0,0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"429\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0418\u0437 \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u0433\u043e \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0443\u044e \u043e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\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-c94610b6f8baef34a1fb4601c148f515_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{l} a_1-2a_2+3a_3= 0 \\\\[2ex] 4a_1-a_3 =0\\\\[2ex] 3a_1+2a_2-4a_3 = 0 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"175\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041f\u043e\u0441\u043b\u0435 \u0442\u043e\u0433\u043e, \u043a\u0430\u043a \u043c\u044b \u0441\u0444\u043e\u0440\u043c\u0443\u043b\u0438\u0440\u043e\u0432\u0430\u043b\u0438 \u0441\u0438\u0441\u0442\u0435\u043c\u0443 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439, \u043d\u0430\u0445\u043e\u0434\u0438\u043c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0441 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0430\u043c\u0438 \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-67678c37fdaf0955ef8bbab8d34379f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} 1&amp;-2&amp;3\\\\[1.1ex] 4&amp;0&amp;-1 \\\\[1.1ex] 3&amp;2&amp;-4 \\end{vmatrix} \\bm{= 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"127\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0412 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u0435\u043d 0, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0442\u0440\u0438 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 <strong>\u0437\u0430\u0432\u0438\u0441\u044f\u0442 \u0434\u0440\u0443\u0433 \u043e\u0442 \u0434\u0440\u0443\u0433\u0430 \u043b\u0438\u043d\u0435\u0439\u043d\u043e<\/strong> .<\/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> \u0414\u043b\u044f \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 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b, \u0430 \u043a\u0430\u043a\u0438\u0435 \u043f\u0430\u0440\u044b \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\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-c53b2414f85df7b5510ea6f379ad9c59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (1,2,-2) \\qquad \\vv{\\text{v}} = (2,4,-3) \\qquad \\vv{\\text{w}} = (-4,-8,6)\" 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\"> \u0421\u0430\u043c\u044b\u0439 \u043f\u0440\u043e\u0441\u0442\u043e\u0439 \u0441\u043f\u043e\u0441\u043e\u0431 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\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 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0439 \u0438\u043b\u0438 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0439, \u2014 \u044d\u0442\u043e \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 \u043e\u043d\u0438.<\/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-2e9f2e572ec99322a57982b9cb393ca8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{1}{2} = \\cfrac{2}{4} \\neq \\cfrac{-2}{-3} \\ \\longrightarrow \\ \\text{LI}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"167\" 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-034dc83f2bfec42f9cf743d295f52feb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{1}{-4} = \\cfrac{2}{-8} \\neq \\cfrac{-2}{6} \\ \\longrightarrow \\ \\text{LI}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"194\" 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-bf4a92d82a160dae8ee8ca41cfad22ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{2}{-4} = \\cfrac{4}{-8} = \\cfrac{-3}{6} = -\\cfrac{1}{2} \\ \\longrightarrow \\ \\text{Proporcionales}\\ \\longrightarrow \\ \\text{LD}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"414\" style=\"vertical-align: -12px;\"><\/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\u043e\u0439 \u043f\u0430\u0440\u043e\u0439 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u0434\u0440\u0443\u0433 \u043e\u0442 \u0434\u0440\u0443\u0433\u0430, \u044f\u0432\u043b\u044f\u0435\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-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-b3184c3260a84d9f7722440a1b95392f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}= -\\cfrac{1}{2} \\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-5a599602f8553abe4f0fb99e3efd3966_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{w}}= -2\\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\"> \u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u043e\u0441\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u043f\u0430\u0440\u044b \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b.<\/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> \u0418\u0437\u0443\u0447\u0438\u0442\u0435 \u043b\u0438\u043d\u0435\u0439\u043d\u0443\u044e \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u0438\u043b\u0438 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0445 4-\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u0434\u0440\u0443\u0433 \u043e\u0442 \u0434\u0440\u0443\u0433\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-32b4b70627510756dee79c34319889d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (0,1,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"89\" 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-fa38827f1af905436c7ac1b64da780d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}} = (-1,-2,0)\" 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-3b827cfdbb2751b83b0dfa8e571f20cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{w}} = (4,1,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"106\" 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-25ba65cf2ebddf211e70958fed7a6dd1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{x}} = (-2,-3,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"116\" 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\"> \u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u0441\u0444\u043e\u0440\u043c\u0443\u043b\u0438\u0440\u0443\u0435\u043c \u0443\u0441\u043b\u043e\u0432\u0438\u0435 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\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-75cb11870b19756a745d82caf5ecba82_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}}+a_4\\vv{\\text{x}}=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"207\" 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-6bd2e86f772066a8ad2255f8dffa054d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1(0,1,2)+a_2(-1,-2,0)+ a_3(4,1,-1)+a_4(-2,-3,2)=(0,0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"506\" 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-192de9f156d81073e6e0b3815fe6703a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(0,a_1,2a_1)+(-a_2,-2a_2,0) +(4a_3,a_3,-a_3)+(-2a_4,-3a_4,2a_4)=(0,0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"572\" 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-828034966309aab74913c929b3781e81_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(-a_2+4a_3-2a_4\\ , \\ a_1-2a_2+a_3-3a_4 \\ , \\ 2a_1-a_3+2a_4)=(0,0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"520\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0412 \u0434\u0430\u043d\u043d\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u043c\u044b \u0438\u043c\u0435\u0435\u043c \u0441\u0438\u0441\u0442\u0435\u043c\u0443 \u0442\u0440\u0435\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u0441 \u0447\u0435\u0442\u044b\u0440\u044c\u043c\u044f \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\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-e9451263e5a31994569292e32666d93e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{l} -a_2+4a_3-2a_4 = 0 \\\\[2ex] a_1-2a_2+a_3-3a_4 =0\\\\[2ex] 2a_1-a_3+2a_4 = 0 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"205\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041c\u044b \u043d\u0435 \u043c\u043e\u0436\u0435\u043c \u0440\u0435\u0448\u0438\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u0432\u0441\u0435\u0439 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0441\u0438\u0441\u0442\u0435\u043c\u044b, \u0442\u0430\u043a \u043a\u0430\u043a \u043c\u043e\u0436\u043d\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u0442\u043e\u043b\u044c\u043a\u043e \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0435 \u043c\u0430\u0442\u0440\u0438\u0446\u044b. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u0434\u043e\u043b\u0436\u043d\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0432\u0441\u0435 \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u044b\u0435 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u0435\u0439 3\u00d73 \u0438 \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c, \u0440\u0430\u0432\u0435\u043d \u043b\u0438 \u043e\u0434\u0438\u043d \u0438\u0437 \u043d\u0438\u0445 0, \u0438 \u0432 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u044b \u0431\u0443\u0434\u0443\u0442 \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b, \u0441 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u0435\u0441\u043b\u0438 \u0432\u0441\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u0438 \u043e\u0442\u043b\u0438\u0447\u043d\u044b \u043e\u0442 0, 4 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u0431\u0443\u0434\u0443\u0442 \u0431\u044b\u0442\u044c \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u043c.<\/p>\n<p class=\"has-text-align-left\"> \u0412\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\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-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-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-488d7848a40aa9a91bd5b3aa1f09b774_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} 0&amp;-1&amp;4\\\\[1.1ex] 1&amp;-2&amp;1 \\\\[1.1ex] 2&amp;0&amp;-1 \\end{vmatrix} =13\\bm{\\neq 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"165\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u043f\u0435\u0440\u0432\u044b\u0445 \u0442\u0440\u0451\u0445 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u043e\u0432 (\u0438\u043b\u0438 \u043f\u0435\u0440\u0432\u044b\u0445 \u0442\u0440\u0451\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432) \u043e\u0442\u043b\u0438\u0447\u0435\u043d \u043e\u0442 \u043d\u0443\u043b\u044f. \u0418\u0442\u0430\u043a, \u0442\u0435\u043f\u0435\u0440\u044c \u043c\u044b \u043f\u043e\u043f\u0440\u043e\u0431\u0443\u0435\u043c \u0441 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u0435\u043c \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\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-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-f76864c5409cf2dea96ed29cc6bf43c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_4:\" 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-d1475a77f10ea0c16147a6f9c3f611b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} 0&amp;-1&amp;-2\\\\[1.1ex] 1&amp;-2&amp;-3 \\\\[1.1ex] 2&amp;0&amp;2 \\end{vmatrix} \\bm{= 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"127\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041c\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u043b\u0438 \u043d\u0443\u043b\u0435\u0432\u043e\u0439 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043d\u0435\u0442 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e\u0441\u0442\u0438 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0442\u044c \u043e\u0441\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u0438, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043c\u044b \u0443\u0436\u0435 \u0437\u043d\u0430\u0435\u043c, \u0447\u0442\u043e 4 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 <strong>\u043b\u0438\u043d\u0435\u0439\u043d\u043e \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b<\/strong> .<\/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 5<\/h3>\n<p> \u0420\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u0439\u0442\u0435 \u0441\u0442\u043e\u0438\u043c\u043e\u0441\u0442\u044c<\/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-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0442\u0430\u043a \u0447\u0442\u043e \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u044b \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\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-edc48924ce57971f9c5940e09d028aff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (3,-1,5)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"103\" 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-88c00cd3b8e4f88f1092a5fb484cd5fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}} = (-2,4,7)\" 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-d2848445bf3f500e9635da849a0fa1d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{w}} = (1,3,k)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"93\" 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\"> \u041f\u0440\u0435\u0436\u0434\u0435 \u0432\u0441\u0435\u0433\u043e \u0441\u0444\u043e\u0440\u043c\u0443\u043b\u0438\u0440\u0443\u0435\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\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-2580c2225e7e01a88d80c323da49b776_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}}=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"159\" 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-b94523fdc15d85da997726f01a1df5b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1(3,-1,5)+a_2(-2,4,7)+ a_3(1,3,k)=(0,0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"370\" 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-78e6c627ddd8e0bd7070c329152ba135_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(3a_1,-a_1,5a_1)+(-2a_2,4a_2,7a_2) + (a_3,3a_3,ka_3)=(0,0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"454\" 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-cccd303f53e73d03d6f47d3694d09b7a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(3a_1-2a_2+a_3 \\ , \\ -a_1+4a_2+3a_3 \\ , \\ 5a_1+7a_2+ka_3)=(0,0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"492\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0418\u0437 \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u0433\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0443\u044e \u043e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\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-16f88cbf406c1faf61307b99179a5de6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{l}3a_1-2a_2+a_3= 0 \\\\[2ex] -a_1+4a_2+3a_3 =0\\\\[2ex] 5a_1+7a_2+ka_3 = 0 \\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\"> \u041f\u043e\u0441\u043b\u0435 \u0442\u043e\u0433\u043e \u043a\u0430\u043a \u043c\u044b \u0441\u0444\u043e\u0440\u043c\u0443\u043b\u0438\u0440\u043e\u0432\u0430\u043b\u0438 \u0441\u0438\u0441\u0442\u0435\u043c\u0443 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439, \u043f\u043e\u043f\u0440\u043e\u0431\u0443\u0435\u043c \u0440\u0435\u0448\u0438\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u0441\u0438\u0441\u0442\u0435\u043c\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-d748080bb1cacc1c80a35ef633a2d85e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} 3&amp;-2&amp;1\\\\[1.1ex] -1&amp;4&amp;3 \\\\[1.1ex] 5&amp;7&amp;k \\end{vmatrix} =10k-120\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"197\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0423\u0442\u0432\u0435\u0440\u0436\u0434\u0435\u043d\u0438\u0435 \u0433\u043e\u0432\u043e\u0440\u0438\u0442 \u043d\u0430\u043c, \u0447\u0442\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u044b \u0434\u043e\u043b\u0436\u043d\u044b \u0431\u044b\u0442\u044c \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u043c\u0438. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u0434\u043e\u043b\u0436\u0435\u043d \u0431\u044b\u0442\u044c \u0440\u0430\u0432\u0435\u043d \u043d\u0443\u043b\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-a0d1aeff1b4ba348b51bb226997d7202_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 10k-120=0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"107\" 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-b98ff23cda28486515d12ef26c8a0e25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 10k=120\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"77\" 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-4177c59fe629665dcf7a57de632b85ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle k=\\cfrac{120}{10}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"62\" style=\"vertical-align: -12px;\"><\/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-32770a08083461fbb6a7260627d6a9c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{k=12}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"50\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u0430 \u0434\u043e\u043b\u0436\u043d\u0430 \u0431\u044b\u0442\u044c \u0440\u0430\u0432\u043d\u0430 12, \u0447\u0442\u043e\u0431\u044b \u0432\u0435\u043a\u0442\u043e\u0440\u044b \u0438\u043c\u0435\u043b\u0438 \u043b\u0438\u043d\u0435\u0439\u043d\u0443\u044e \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c.<\/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 \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u044f\u0435\u043c, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u0435 \u0438 \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u044b. \u0412\u044b \u0442\u0430\u043a\u0436\u0435 \u0443\u0432\u0438\u0434\u0438\u0442\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u0442\u043e\u0433\u043e, \u043a\u0430\u043a \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043b\u0438 \u043d\u0430\u0431\u043e\u0440 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u043c \u0438\u043b\u0438 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u043c. \u0410, \u043a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u043f\u043e\u0448\u0430\u0433\u043e\u0432\u044b\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f \u0438 \u0440\u0435\u0448\u0430\u0435\u043c\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u043d\u0430 \u043b\u0438\u043d\u0435\u0439\u043d\u0443\u044e \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u0438 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c. \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u044b? \u041c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u043e \u0441\u0432\u043e\u0431\u043e\u0434\u043d\u044b\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u043b\u0438\u043d\u0435\u0439\u043d\u043e \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u043c, \u0435\u0441\u043b\u0438 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ru\/%d0%bd%d0%b5%d0%b7%d0%b0%d0%b2%d0%b8%d1%81%d0%b8%d0%bc%d1%8b%d0%b5-%d0%b8-%d0%bb%d0%b8%d0%bd%d0%b5%d0%b8%d0%bd%d0%be-%d0%b7%d0%b0%d0%b2%d0%b8%d1%81%d0%b8%d0%bc%d1%8b%d0%b5-%d0%b2%d0%b5%d0%ba%d1%82\/\"> <span class=\"screen-reader-text\">\u041b\u0438\u043d\u0435\u0439\u043d\u043e \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u0435 \u0438 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u044b (\u043b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u0438 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c)<\/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-72","post","type-post","status-publish","format-standard","hentry","category-22"],"yoast_head":"<!-- This site is optimized 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