{"id":70,"date":"2023-09-16T13:04:23","date_gmt":"2023-09-16T13:04:23","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e5%90%91%e9%87%8f%e7%9a%84%e7%ba%bf%e6%80%a7%e7%bb%84%e5%90%88%e7%a4%ba%e4%be%8b%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%bb%83%e4%b9%a0\/"},"modified":"2023-09-16T13:04:23","modified_gmt":"2023-09-16T13:04:23","slug":"%e5%90%91%e9%87%8f%e7%9a%84%e7%ba%bf%e6%80%a7%e7%bb%84%e5%90%88%e7%a4%ba%e4%be%8b%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%bb%83%e4%b9%a0","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e5%90%91%e9%87%8f%e7%9a%84%e7%ba%bf%e6%80%a7%e7%bb%84%e5%90%88%e7%a4%ba%e4%be%8b%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%bb%83%e4%b9%a0\/","title":{"rendered":"\u5411\u91cf\u7684\u7ebf\u6027\u7ec4\u5408"},"content":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u627e\u5230\u5411\u91cf\u4e4b\u95f4\u7ebf\u6027\u7ec4\u5408\u542b\u4e49\u7684\u89e3\u91ca\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u5982\u4f55\u5c06\u5411\u91cf\u8868\u793a\u4e3a\u7ebf\u6027\u7ec4\u5408\u7684\u793a\u4f8b\uff0c\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u901a\u8fc7\u7ec3\u4e60\u548c\u9010\u6b65\u89e3\u51b3\u7684\u95ee\u9898\u8fdb\u884c\u7ec3\u4e60\u3002 <\/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>\u4ec0\u4e48\u662f\u5411\u91cf\u7684\u7ebf\u6027\u7ec4\u5408\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u7ebf\u6027\u7ec4\u5408\u7684\u5b9a\u4e49\u5982\u4e0b\uff1a <\/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\">\u4e00\u7ec4\u5411\u91cf\u7684<strong>\u7ebf\u6027\u7ec4\u5408<\/strong>\u662f\u5c06\u7ec4\u4e2d\u6240\u6709\u5411\u91cf\u4e58\u4ee5\u6807\u91cf\uff08\u5b9e\u6570\uff09\u76f8\u52a0\u800c\u5f97\u5230\u7684\u5411\u91cf\u3002<\/p>\n<p style=\"text-align:left\">\u6362\u53e5\u8bdd\u8bf4\uff0c\u7ed9\u5b9a\u4e00\u7ec4\u5411\u91cf<\/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>\u5b83\u4eec\u7684\u7ebf\u6027\u7ec4\u5408\u662f\uff1a<\/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\">\u5176\u4e2d\u7cfb\u6570<\/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>\u8fd9\u4e9b\u662f\u5b9e\u6570\u3002<\/p>\n<\/div>\n<p>\u56e0\u6b64\uff0c\u4f5c\u4e3a\u5176\u4ed6\u5411\u91cf\u7684\u7ebf\u6027\u7ec4\u5408\u7684\u5411\u91cf\u610f\u5473\u7740\u7b2c\u4e00\u4e2a\u5411\u91cf\u53ef\u4ee5\u7528\u7b2c\u4e8c\u4e2a\u5411\u91cf\u6765\u8868\u8fbe\u3002<\/p>\n<p>\u901a\u8fc7\u5728\u5e73\u9762\u4e0a\u7ed8\u5236\u4e00\u4e2a\u5411\u91cf\uff08\u4e24\u4e2a\u5411\u91cf\u7684\u7ebf\u6027\u7ec4\u5408\uff09\u53ef\u4ee5\u66f4\u597d\u5730\u7406\u89e3\u8fd9\u4e2a\u6982\u5ff5\uff1a <\/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=\"r3 \u4e2d\u5411\u91cf\u7684\u7ebf\u6027\u7ec4\u5408\" class=\"wp-image-781\" width=\"405\" height=\"408\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p>\u6b63\u5982\u60a8\u5728\u4e0a\u9762\u7684\u56fe\u5f62\u8868\u793a\u4e2d\u770b\u5230\u7684\uff0c\u5411\u91cf<\/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>\u53ef\u4ee5\u4ece\u5411\u91cf\u4e2d\u83b7\u5f97<\/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>\u548c<\/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>\u6267\u884c\u5411\u91cf\u8fd0\u7b97\u3002\u56e0\u6b64\uff0c\u5411\u91cf<\/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>\u662f\u5176\u4ed6\u4e24\u4e2a\u5411\u91cf\u7684\u7ebf\u6027\u7ec4\u5408\u3002<\/p>\n<p>\u9700\u8981\u5f3a\u8c03\u7684\u662f\uff0c\u8fd9\u79cd\u7ebf\u6027\u7ec4\u5408\u662f<strong>\u552f\u4e00\u7684<\/strong>\uff0c\u6216\u8005\u8bf4\uff0c\u6bcf\u4e2a\u5411\u91cf\u53ea\u6709\u4e00\u4e2a\u53ef\u884c\u7684\u7ebf\u6027\u7ec4\u5408\u3002\u56e0\u4e3a\u6309\u7167\u524d\u9762\u7684\u4f8b\u5b50\uff0c\u5982\u679c\u6211\u4eec\u4e58\u4ee5<\/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>\u5bf9\u4e8e 6 \u800c\u4e0d\u662f 4\uff0c\u6211\u4eec\u5c06\u83b7\u5f97\u53e6\u4e00\u4e2a\u4e0d\u540c\u7684\u5411\u91cf\u3002 <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-106\"><\/div>\n<\/div>\n<p>\u6b64\u5916\uff0c\u5e73\u9762\uff08R2\uff09\u4e2d\u7ebf\u6027\u7ec4\u5408\u7684\u5c5e\u6027\u4e4b\u4e00\u662f\uff0c\u5982\u679c\u4efb\u4f55\u5411\u91cf\u5177\u6709\u4e0d\u540c\u7684\u65b9\u5411\uff0c\u5373\u5982\u679c\u5b83\u4eec\u4e0d\u5e73\u884c\uff0c\u5219\u4efb\u4f55\u5411\u91cf\u90fd\u53ef\u4ee5\u4f5c\u4e3a\u5176\u4ed6\u4e24\u4e2a\u5411\u91cf\u7684\u7ebf\u6027\u7ec4\u5408\u3002<\/p>\n<p>\u53e6\u5916\uff0c\u6709\u65f6\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u8089\u773c\u8bc6\u522b\u51fa\u4e24\u4e2a\u5411\u91cf\u662f\u7ebf\u6027\u7ec4\u5408\u3002\u8981\u505a\u5230\u8fd9\u4e00\u70b9\uff0c\u5176\u7ec4\u6210\u90e8\u5206\u6210<strong>\u6bd4\u4f8b<\/strong>\u5c31\u8db3\u591f\u4e86\u3002\u4f8b\u5982\uff0c\u4ee5\u4e0b\u4e24\u4e2a\u5411\u91cf\u7684\u5750\u6807\u6210\u6bd4\u4f8b\uff0c\u56e0\u6b64\u5411\u91cf\u662f\u7ebf\u6027\u7ec4\u5408\uff1a<\/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>\u6700\u540e\uff0c\u65e0\u8bba\u662f\u5728\u4e8c\u7ef4\uff08R2 \u4e2d\uff09\u8fd8\u662f\u4e09\u7ef4\uff08R3 \u4e2d\uff09\u5411\u91cf\u7a7a\u95f4\u4e2d\uff0c\u5982\u679c\u4e00\u7ec4\u5411\u91cf\u5185\u5b58\u5728\u7ebf\u6027\u7ec4\u5408\uff0c\u5219\u610f\u5473\u7740\u5b83\u4eec\u5f7c\u6b64<strong>\u7ebf\u6027\u76f8\u5173<\/strong>\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5982\u679c\u5411\u91cf\u4e4b\u95f4\u4e0d\u53ef\u80fd\u5b58\u5728\u7ebf\u6027\u7ec4\u5408\uff0c\u5219\u610f\u5473\u7740\u5b83\u4eec\u662f<strong>\u7ebf\u6027\u65e0\u5173\u7684<\/strong>\u3002<\/p>\n<p>\u5982\u679c\u60a8\u4e0d\u5b8c\u5168\u6e05\u695a\u6700\u540e\u4e00\u4e2a\u6982\u5ff5\uff0c\u6211\u4eec\u5efa\u8bae\u60a8\u67e5\u770b\u6211\u4eec\u5bf9<a href=\"https:\/\/mathority.org\/cn\/\u72ec\u7acb\u548c\u7ebf\u6027\u76f8\u5173\u5411\u91cf-\u72ec\u7acb-\u7ebf\u6027\u76f8\u5173\/\">\u7ebf\u6027\u76f8\u5173\u5411\u91cf\u548c\u72ec\u7acb\u5411\u91cf<\/a>\u7684\u89e3\u91ca\uff0c\u5728\u8fd9\u91cc\u60a8\u5c06\u627e\u5230\u7ebf\u6027\u76f8\u5173\u6216\u72ec\u7acb\u5411\u91cf\u7684\u542b\u4e49\u3001\u6bcf\u79cd\u7c7b\u578b\u7684\u793a\u4f8b\u4ee5\u53ca\u5b83\u4eec\u4e4b\u95f4\u7684\u5dee\u5f02\u3002 \u3002\u8fd9\u4e2a\u6982\u5ff5\u88ab\u5e7f\u6cdb\u4f7f\u7528\uff0c\u4e8b\u5b9e\u4e0a\uff0c\u5b83\u5728\u8003\u8bd5\u4e2d\u4e5f\u7ecf\u5e38\u88ab\u95ee\u5230\uff0c\u6240\u4ee5\u5145\u5206\u7406\u89e3\u5b83\u5f88\u91cd\u8981\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-expresar-un-vector-como-combinacion-lineal-de-otros-vectores\"><\/span>\u5982\u4f55\u5c06\u5411\u91cf\u8868\u793a\u4e3a\u5176\u4ed6\u5411\u91cf\u7684\u7ebf\u6027\u7ec4\u5408<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>\u7136\u540e\u6211\u4eec\u5c06\u770b\u5230\u5982\u4f55\u89e3\u51b3\u4e00\u4e2a\u5178\u578b\u7684\u95ee\u9898\uff0c\u5176\u4e2d\u8981\u6c42\u6211\u4eec\u627e\u5230\u5411\u91cf\u7684\u7ebf\u6027\u7ec4\u5408\u3002<\/p>\n<ul>\n<li>\u8868\u8fbe\u5411\u91cf\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>\u4f5c\u4e3a\u7ebf\u6027\u7ec4\u5408<\/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>\u548c<\/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>\u4f7f\u5f97\u5411\u91cf<\/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>\u662f\u5176\u4ed6\u5411\u91cf\u7684\u7ebf\u6027\u7ec4\u5408\uff0c\u5fc5\u987b\u6ee1\u8db3\u4ee5\u4e0b\u7b49\u5f0f\uff1a<\/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>\u5176\u4e2d\u7cfb\u6570<\/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>\u548c<\/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>\u8fd9\u4e9b\u90fd\u662f\u6211\u4eec\u5fc5\u987b\u627e\u5230\u7684\u672a\u77e5\u6570\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u6211\u4eec\u7528\u6bcf\u4e2a\u5411\u91cf\u7684\u5750\u6807\u66ff\u6362\u5b83\uff1a<\/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>\u6211\u4eec\u5c06\u6bcf\u4e2a\u5411\u91cf\u4e58\u4ee5\u5176\u7cfb\u6570\uff1a<\/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>\u6211\u4eec\u6dfb\u52a0\u5411\u91cf\uff1a<\/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>\u6bcf\u4e2a\u5de6\u5750\u6807\u5fc5\u987b\u7b49\u4e8e\u6bcf\u4e2a\u53f3\u5750\u6807\u3002\u56e0\u6b64\u6211\u4eec\u6709 3 \u4e2a\u65b9\u7a0b\uff1a<\/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>\u5269\u4e0b\u7684\u5c31\u662f\u6c42\u89e3\u6240\u83b7\u5f97\u7684\u65b9\u7a0b\u7ec4\u3002\u4e3a\u6b64\uff0c\u8bf7\u4f7f\u7528\u60a8\u559c\u6b22\u7684\u65b9\u6cd5\uff08\u66ff\u6362\u6cd5\u3001\u514b\u83b1\u9ed8\u6cd5\u5219\u3001\u9ad8\u65af-\u4e54\u4e39\u6cd5\u7b49\uff09\uff0c\u5728\u672c\u4f8b\u4e2d\u6211\u4eec\u5c06\u4f7f\u7528\u9ad8\u65af\u6cd5\uff1a <\/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>\u56e0\u6b64\uff0c\u83b7\u5f97\u7684\u6b65\u9aa4\u7cfb\u7edf\u662f\uff1a<\/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>\u6211\u4eec\u73b0\u5728\u8981\u505a\u7684\u5c31\u662f\u6f84\u6e05\u672a\u77e5\u5e76\u53d1\u73b0\u5b83\u7684\u4ef7\u503c\u3002\u6240\u4ee5\u4ece\u6700\u540e\u4e00\u4e2a\u65b9\u7a0b\u6211\u4eec\u53d1\u73b0<\/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>\u6839\u636e\u7cfb\u7edf\u7684\u7b2c\u4e8c\u4e2a\u65b9\u7a0b\uff0c\u6211\u4eec\u8ba1\u7b97\u51fa<\/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>\u6700\u540e\uff0c\u4ece\u6b65\u9aa4\u7cfb\u7edf\u7684\u7b2c\u4e00\u4e2a\u65b9\u7a0b\uff0c\u6211\u4eec\u627e\u5230\u672a\u77e5\u6570<\/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>\u56e0\u6b64\uff0c\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u89e3\u4e3a\uff1a<\/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>\u6240\u4ee5\u5411\u91cf<\/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>\u53ef\u4ee5\u7528\u5982\u4e0b\u7684\u7ebf\u6027\u7ec4\u5408\u6765\u8868\u793a\uff1a <\/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>\u56e0\u6b64\uff0c\u5411\u91cf\u4e4b\u95f4\u5b9e\u9645\u4e0a\u5b58\u5728\u7ebf\u6027\u76f8\u5173\u6027\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5982\u679c\u6ca1\u6709\u83b7\u5f97\u65b9\u7a0b\u7ec4\u7684\u89e3\uff0c\u5219\u8fd9\u610f\u5473\u7740\u5411\u91cf<\/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>\u5b83\u76f8\u5bf9\u4e8e\u5176\u4ed6\u5411\u91cf\u7ebf\u6027\u65e0\u5173\uff0c\u56e0\u6b64\uff0c\u4e0d\u53ef\u80fd\u901a\u8fc7\u7ebf\u6027\u7ec4\u5408\u4ece\u5176\u4ed6\u5411\u91cf\u83b7\u5f97\u6240\u8ff0\u5411\u91cf\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-combinacion-lineal-de-vectores\"><\/span>\u89e3\u51b3\u4e86\u5411\u91cf\u7ebf\u6027\u7ec4\u5408\u7684\u7ec3\u4e60<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u5728\u4ee5\u4e0b\u4e09\u4e2a\u5411\u91cf\u4e2d\uff0c\u6307\u793a\u54ea\u4e9b\u5bf9\u662f\u5f7c\u6b64\u7684\u7ebf\u6027\u7ec4\u5408\u3002\u53e6\u5916\uff0c\u6c42\u51fa\u6240\u8ff0\u5411\u91cf\u5bf9\u7684\u7ebf\u6027\u7ec4\u5408\u5173\u7cfb\u3002 <\/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>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u8981\u77e5\u9053\u4e00\u5bf9\u5411\u91cf\u662f\u5426\u662f\u7ebf\u6027\u7ec4\u5408\uff0c\u6211\u4eec\u5fc5\u987b\u770b\u770b\u5b83\u4eec\u7684\u5750\u6807\u662f\u5426\u6210\u6bd4\u4f8b\u3002<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u9996\u5148\u68c0\u67e5\u5411\u91cf<\/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>\u4e0e\u5411\u91cf<\/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\">\u5176\u6b21\uff0c\u6211\u4eec\u68c0\u67e5\u5411\u91cf<\/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>\u4e0e\u5411\u91cf<\/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\">\u6700\u540e\uff0c\u6211\u4eec\u6d4b\u8bd5\u5411\u91cf<\/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>\u4e0e\u5411\u91cf<\/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\">\u6240\u4ee5\u552f\u4e00\u4e00\u5bf9\u7ebf\u6027\u7ec4\u5408\u7684\u5411\u91cf\u662f<\/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>\u548c<\/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>\u6b64\u5916\uff0c\u5b83\u4eec\u7684\u5173\u7cfb\u5982\u4e0b\uff1a<\/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\">\u6216\u540c\u7b49\u5b66\u5386\uff1a<\/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\">\u5c3d\u7ba1\u8be5\u8bed\u53e5\u4e0d\u8981\u6c42\u5b83\uff0c\u4f46\u76f8\u4e92\u7ebf\u6027\u4f9d\u8d56\u7684\u552f\u4e00\u5411\u91cf\u662f<\/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>\u548c<\/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>\u56e0\u4e3a\u5b83\u4eec\u4e4b\u95f4\u5b58\u5728\u7ebf\u6027\u7ec4\u5408\u3002\u5176\u4ed6\u5bf9\u662f\u7ebf\u6027\u72ec\u7acb\u7684\uff0c\u56e0\u4e3a\u5b83\u4eec\u4e0d\u80fd\u7ebf\u6027\u7ec4\u5408\u3002<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e602<\/h3>\n<p>\u6c42\u5411\u91cf\u4e4b\u95f4\u7684\u7ebf\u6027\u5173\u7cfb<\/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>\u548c\u5411\u91cf\u96c6<\/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>\u548c<\/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>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u4f7f\u5f97\u5411\u91cf<\/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>\u662f\u5176\u4ed6\u5411\u91cf\u7684\u7ebf\u6027\u7ec4\u5408\uff0c\u5fc5\u987b\u6ee1\u8db3\u4ee5\u4e0b\u7b49\u5f0f\uff1a<\/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\">\u56e0\u6b64\uff0c\u6211\u4eec\u7528\u6bcf\u4e2a\u5411\u91cf\u7684\u5750\u6807\u66ff\u6362\u5b83\uff1a<\/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\">\u6211\u4eec\u5c06\u6bcf\u4e2a\u5411\u91cf\u4e58\u4ee5\u5176\u5e38\u6570\uff1a<\/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\">\u6211\u4eec\u6dfb\u52a0\u5411\u91cf\uff1a<\/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\">\u56e0\u6b64\u6211\u4eec\u5f97\u5230\u4ee5\u4e0b\u65b9\u7a0b\u7ec4\uff1a<\/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\">\u6211\u4eec\u7528\u9ad8\u65af\u65b9\u6cd5\u6c42\u89e3\u5f97\u5230\u7684\u7cfb\u7edf\uff1a <\/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\">\u56e0\u6b64\uff0c\u83b7\u5f97\u7684\u6b65\u9aa4\u7cfb\u7edf\u662f\uff1a<\/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\">\u6211\u4eec\u73b0\u5728\u8981\u505a\u7684\u5c31\u662f\u6f84\u6e05\u672a\u77e5\u5e76\u53d1\u73b0\u5b83\u7684\u4ef7\u503c\u3002\u6240\u4ee5\u4ece\u6700\u540e\u4e00\u4e2a\u65b9\u7a0b\u6211\u4eec\u53d1\u73b0<\/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\">\u6839\u636e\u7cfb\u7edf\u7684\u7b2c\u4e8c\u4e2a\u65b9\u7a0b\uff0c\u6211\u4eec\u8ba1\u7b97\u51fa<\/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\">\u6700\u540e\uff0c\u4ece\u6b65\u9aa4\u7cfb\u7edf\u7684\u7b2c\u4e00\u4e2a\u65b9\u7a0b\uff0c\u6211\u4eec\u627e\u5230\u672a\u77e5\u6570<\/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\">\u56e0\u6b64\uff0c\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u89e3\u4e3a\uff1a<\/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\">\u6240\u4ee5\u5411\u91cf<\/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>\u53ef\u4ee5\u7528\u5982\u4e0b\u7684\u7ebf\u6027\u7ec4\u5408\u6765\u8868\u793a\uff1a <\/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\">\u7ec3\u4e603<\/h3>\n<p>\u8868\u8fbe\u5411\u91cf<\/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>\u4f5c\u4e3a\u5411\u91cf\u7684\u7ebf\u6027\u7ec4\u5408<\/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>\u548c<\/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>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u6211\u4eec\u63d0\u51fa\u5173\u4e8e\u5411\u91cf\u7684\u7ebf\u6027\u7ec4\u5408\u65b9\u7a0b<\/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\">\u56e0\u6b64\uff0c\u6211\u4eec\u7528\u6bcf\u4e2a\u5411\u91cf\u7684\u5206\u91cf\u66ff\u6362\u5b83\uff1a<\/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\">\u6211\u4eec\u5c06\u6bcf\u4e2a\u5411\u91cf\u4e58\u4ee5\u5176\u5404\u81ea\u7684\u672a\u77e5\u6570\uff1a<\/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\">\u6211\u4eec\u8fdb\u884c\u5411\u91cf\u7684\u52a0\u6cd5\uff1a<\/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\">\u56e0\u6b64\u6211\u4eec\u5f97\u5230\u4e86\u5982\u4e0b\u65b9\u7a0b\u7ec4\uff1a<\/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\">\u6211\u4eec\u7528\u9ad8\u65af\u65b9\u6cd5\u6c42\u89e3\u5f97\u5230\u7684\u7cfb\u7edf\uff1a <\/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\">\u56e0\u6b64\uff0c\u83b7\u5f97\u7684\u6b65\u9aa4\u7cfb\u7edf\u662f\uff1a<\/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\">\u6211\u4eec\u73b0\u5728\u8981\u505a\u7684\u5c31\u662f\u6f84\u6e05\u672a\u77e5\u5e76\u53d1\u73b0\u5b83\u7684\u4ef7\u503c\u3002\u6240\u4ee5\u4ece\u6700\u540e\u4e00\u4e2a\u65b9\u7a0b\u6211\u4eec\u53d1\u73b0<\/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\">\u4ece\u7cfb\u7edf\u7684\u7b2c\u4e8c\u4e2a\u65b9\u7a0b\uff0c\u6211\u4eec\u627e\u5230\u503c<\/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\">\u6700\u540e\uff0c\u4ece\u6b65\u9aa4\u7cfb\u7edf\u7684\u7b2c\u4e00\u4e2a\u65b9\u7a0b\uff0c\u6211\u4eec\u6c42\u89e3\u672a\u77e5\u6570<\/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\">\u56e0\u6b64\uff0c\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u89e3\u4e3a\uff1a<\/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\">\u6240\u4ee5\u5411\u91cf<\/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>\u53ef\u4ee5\u901a\u8fc7\u7ebf\u6027\u7ec4\u5408\u5176\u4ed6\u5411\u91cf\u6765\u8868\u793a\uff1a <\/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\">\u7ec3\u4e604<\/h3>\n<p>\u5224\u65ad\u5411\u91cf\u662f\u5426<\/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>\u53ef\u4ee5\u8868\u793a\u4e3a\u5411\u91cf\u7684\u7ebf\u6027\u7ec4\u5408<\/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>\u548c<\/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>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u627e\u5230\u8fde\u63a5\u5b83\u4eec\u7684\u8868\u8fbe\u5f0f\u3002 <\/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>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u4f7f\u5f97\u5411\u91cf<\/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>\u662f\u5176\u4ed6\u5411\u91cf\u7684\u7ebf\u6027\u7ec4\u5408\uff0c\u5fc5\u987b\u6ee1\u8db3\u4ee5\u4e0b\u7b49\u5f0f\uff1a<\/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\">\u56e0\u6b64\uff0c\u6211\u4eec\u7528\u6bcf\u4e2a\u5411\u91cf\u7684\u5750\u6807\u66ff\u6362\u5b83\uff1a<\/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\">\u6211\u4eec\u5c06\u6bcf\u4e2a\u5411\u91cf\u4e58\u4ee5\u5176\u7cfb\u6570\uff1a<\/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\">\u6211\u4eec\u6dfb\u52a0\u5411\u91cf\uff1a<\/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\">\u56e0\u6b64\uff0c\u524d\u9762\u7684\u8868\u8fbe\u5f0f\u7b49\u6548\u4e8e\u4ee5\u4e0b\u65b9\u7a0b\u7ec4\uff1a<\/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\">\u6211\u4eec\u73b0\u5728\u7528\u9ad8\u65af\u65b9\u6cd5\u6c42\u89e3\u5f97\u5230\u7684\u7cfb\u7edf\uff1a <\/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\">\u56e0\u6b64\u6211\u4eec\u5f97\u5230\u4e86\u5982\u4e0b\u65b9\u7a0b\u7ec4\uff1a<\/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\">\u7136\u800c\uff0c\u6700\u540e\u4e00\u4e2a\u65b9\u7a0b\u6c38\u8fdc\u65e0\u6cd5\u6ee1\u8db3\uff0c\u56e0\u4e3a\u65e0\u8bba\u672a\u77e5\u6570\u53d6\u4ec0\u4e48\u503c\uff0c0 \u6c38\u8fdc\u4e0d\u4f1a\u7b49\u4e8e -30\u3002\u56e0\u6b64\uff0c\u7cfb\u7edf\u65e0\u89e3\uff0c\u8fd9\u610f\u5473\u7740<strong>\u6ca1\u6709\u7ebf\u6027\u7ec4\u5408<\/strong>\u6765\u8ba1\u7b97\u5411\u91cf<\/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>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u627e\u5230\u5411\u91cf\u4e4b\u95f4\u7ebf\u6027\u7ec4\u5408\u542b\u4e49\u7684\u89e3\u91ca\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u5982\u4f55\u5c06\u5411\u91cf\u8868\u793a\u4e3a\u7ebf\u6027\u7ec4\u5408\u7684\u793a\u4f8b\uff0c\u6b64\u5916\uff0c\u60a8\u5c06\u80fd &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e5%90%91%e9%87%8f%e7%9a%84%e7%ba%bf%e6%80%a7%e7%bb%84%e5%90%88%e7%a4%ba%e4%be%8b%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%bb%83%e4%b9%a0\/\"> <span class=\"screen-reader-text\">\u5411\u91cf\u7684\u7ebf\u6027\u7ec4\u5408<\/span> \u67e5\u770b\u5168\u6587 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