{"id":293,"date":"2023-07-06T16:17:35","date_gmt":"2023-07-06T16:17:35","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e4%b9%94%e4%b8%b9%e9%ab%98%e6%96%af%e6%96%b9%e6%b3%95%e5%8f%8a%e5%85%b6%e7%a4%ba%e4%be%8b%e5%92%8c%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%9a%84%e7%bb%83%e4%b9%a0\/"},"modified":"2023-07-06T16:17:35","modified_gmt":"2023-07-06T16:17:35","slug":"%e4%b9%94%e4%b8%b9%e9%ab%98%e6%96%af%e6%96%b9%e6%b3%95%e5%8f%8a%e5%85%b6%e7%a4%ba%e4%be%8b%e5%92%8c%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%9a%84%e7%bb%83%e4%b9%a0","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e4%b9%94%e4%b8%b9%e9%ab%98%e6%96%af%e6%96%b9%e6%b3%95%e5%8f%8a%e5%85%b6%e7%a4%ba%e4%be%8b%e5%92%8c%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%9a%84%e7%bb%83%e4%b9%a0\/","title":{"rendered":"\u9ad8\u65af\u65b9\u6cd5\u2014\u2014\u4e54\u4e39"},"content":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u4e86\u89e3\u4ec0\u4e48\u662f Gauss-Jordan \u65b9\u6cd5\u4ee5\u53ca\u5982\u4f55\u4f7f\u7528\u9ad8\u65af\u65b9\u6cd5\u6c42\u89e3\u65b9\u7a0b\u7ec4\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u5c06\u627e\u5230\u4f7f\u7528\u9ad8\u65af\u65b9\u6cd5\u7684\u7cfb\u7edf\u7684\u793a\u4f8b\u548c\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\uff0c\u4ee5\u4fbf\u60a8\u53ef\u4ee5\u5b8c\u7f8e\u5730\u7ec3\u4e60\u548c\u7406\u89e3\u5b83\u3002<\/p>\n<h2 class=\"wp-block-heading\">\u9ad8\u65af\u6cd5\u662f\u4ec0\u4e48\uff1f<\/h2>\n<p> <strong>Gauss-Jordan \u65b9\u6cd5<\/strong>\u662f\u7528\u4e8e\u6c42\u89e3\u5177\u6709 3 \u4e2a\u672a\u77e5\u6570\u7684\u65b9\u7a0b\u7ec4\u7684\u8fc7\u7a0b\uff0c\u4e5f\u5c31\u662f\u8bf4\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-088146ef83bbd007e82aca8189434c25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{r} 3x-4y+5z=10 \\\\[2ex] x+5y-2z=4 \\\\[2ex] -x+4y+2z=-1 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"170\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-background\" style=\"background-color:#dff6ff\">\u9ad8\u65af\u65b9\u6cd5\u7684\u76ee\u6807\u662f\u5c06\u521d\u59cb\u65b9\u7a0b\u7ec4\u8f6c\u6362\u4e3a<strong>\u9636\u68af\u65b9\u7a0b\u7ec4<\/strong>\uff0c\u5373\u6bcf\u4e2a\u65b9\u7a0b\u7684\u672a\u77e5\u6570\u90fd\u6bd4\u524d\u4e00\u4e2a\u65b9\u7a0b\u5c11\u7684\u4e00\u4e2a\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-10926b0856ae512c737ae924bd9413a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{r} a_1x+b_1y+c_1z=d_1 \\\\[2ex] a_2x+b_2y+c_2z=d_2 \\\\[2ex] a_3x+b_3y+c_3z=d_3 \\end{array} \\right\\} \\ \\bm{\\longrightarrow}   \\left. \\begin{array}{r} A_1x+B_1y+C_1z=D_1 \\\\[2ex] B_2y+C_2z=D_2 \\\\[2ex] C_3z=D_3 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"436\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u7136\u800c\uff0c\u8981\u505a\u5230\u8fd9\u4e00\u70b9\uff0c\u60a8\u5fc5\u987b\u9996\u5148\u77e5\u9053\u5982\u4f55<strong>\u4ee5\u77e9\u9635\u5f62\u5f0f\u8868\u8fbe\u65b9\u7a0b\u7ec4<\/strong>\u4ee5\u53ca\u8be5\u77e9\u9635\u4e0a<strong>\u5141\u8bb8\u7684\u53d8\u6362<\/strong>\u3002\u6240\u4ee5\u6211\u4eec\u4e4b\u524d\u4f1a\u89e3\u91ca\u8fd9\u4e24\u4ef6\u4e8b\uff0c\u7136\u540e\u6211\u4eec\u4f1a\u770b\u5230\u5982\u4f55\u4f7f\u7528<strong>\u9ad8\u65af\u65b9\u6cd5\u7a0b\u5e8f<\/strong>\u3002<\/p>\n<h2 class=\"wp-block-heading\">\u7cfb\u7edf\u6269\u5c55\u77e9\u9635<\/h2>\n<p class=\"has-background\" style=\"background-color:#dff6ff\">\u5728\u4e86\u89e3\u7cfb\u7edf\u5982\u4f55\u6c42\u89e3\u4e4b\u524d\uff0c\u60a8\u5fc5\u987b\u77e5\u9053<strong>\u65b9\u7a0b\u7ec4\u53ef\u4ee5\u7528\u77e9\u9635\u7684\u5f62\u5f0f\u8868\u793a\uff1a<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-891f4f92ba63784e78eefc68d49377b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u653e\u5728\u7b2c\u4e00\u5217\uff0c\u7cfb\u6570<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f731d739f7ff6bfef57b5a830dbe13aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u5728\u7b2c\u4e8c\u5217\u4e2d\uff0c\u7cfb\u6570<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4586e340cb83d5b642972e97a288fec2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u7b2c\u4e09\u5217\u4e2d\u7684\u6570\u5b57\u548c\u7b2c\u56db\u5217\u4e2d\u6ca1\u6709\u672a\u77e5\u6570\u7684\u6570\u5b57\u3002<\/p>\n<p>\u4f8b\u5982\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\/resoudre-un-systeme-d-equations-par-la-methode-de-gauss.webp\" alt=\"\u9ad8\u65af\u6cd5\" class=\"wp-image-4379\" width=\"422\" height=\"415\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\">\u5141\u8bb8\u7684\u884c\u8f6c\u6362<\/h2>\n<p>\u4e3a\u4e86\u5c06\u65b9\u7a0b\u7ec4\u8f6c\u6362\u4e3a\u7f29\u653e\u7cfb\u7edf\uff0c\u53ef\u4ee5\u5bf9\u4e0e\u8be5\u7cfb\u7edf\u76f8\u5173\u7684\u77e9\u9635\u6267\u884c\u4ee5\u4e0b\u64cd\u4f5c\u4e4b\u4e00\uff1a<\/p>\n<ul>\n<li><strong><span style=\"color:#1976d2\">\u66f4\u6539\u77e9\u9635\u4e2d\u7684\u884c\u987a\u5e8f<\/span><\/strong>\u3002<\/li>\n<\/ul>\n<p>\u4f8b\u5982\uff0c\u6211\u4eec\u53ef\u4ee5\u66f4\u6539\u77e9\u9635\u7b2c 2 \u884c\u548c\u7b2c 3 \u884c\u7684\u987a\u5e8f\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-ee0e251559ef9dfd02c9b0105f934af8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} 3 &amp; 5 &amp; -2 &amp; 1 \\\\[2ex] -2 &amp; 4 &amp; -1 &amp; 2 \\\\[2ex] 6 &amp; 1 &amp; -3 &amp; 10 \\end{array} \\right)  \\begin{array}{c} \\\\[2ex] \\xrightarrow{ f_2 \\rightarrow f_3}} \\\\[2ex] \\xrightarrow{ f_3 \\rightarrow f_2}} \\end{array} \\left( \\begin{array}{ccc|c} 3 &amp; 5 &amp; -2 &amp; 1 \\\\[2ex] 6 &amp; 1 &amp; -3 &amp; 10 \\\\[2ex] -2 &amp; 4 &amp; -1 &amp; 2 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"98\" width=\"399\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5c06\u4e00\u884c\u4e2d\u7684\u6240\u6709\u9879<strong><span style=\"color:#1976d2\">\u4e58\u4ee5\u6216\u9664\u4ee5<\/span><\/strong>0 \u4ee5\u5916\u7684\u6570\u5b57\u3002<\/li>\n<\/ul>\n<p>\u4f8b\u5982\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u7b2c 1 \u884c\u4e58\u4ee5 4\uff0c\u5e76\u5c06\u7b2c 3 \u884c\u9664\u4ee5 2\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-0e1f081c9056075ede064b2e5c9e4193_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} 1 &amp; -2 &amp; 3 &amp; 1 \\\\[2ex] 3 &amp; -1 &amp; 5 &amp; -3 \\\\[2ex] 2 &amp; -4 &amp; -2 &amp; 6 \\end{array} \\right) \\begin{array}{c}  \\xrightarrow{4  f_1} \\\\[2ex]  \\\\[2ex] \\xrightarrow{ f_3 \/ 2} \\end{array} \\left( \\begin{array}{ccc|c} 4 &amp; -8 &amp; 12 &amp; 4 \\\\[2ex] 3 &amp; -1 &amp; 5 &amp; -3 \\\\[2ex] 1 &amp; -2 &amp; -1 &amp; 3 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"103\" width=\"396\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li><strong><span style=\"color:#1976d2\">\u5c06\u4e00\u884c\u66ff\u6362<\/span><\/strong>\u4e3a\u540c\u4e00\u884c\u52a0\u4e0a\u53e6\u4e00\u884c\u4e58\u4ee5\u4e00\u4e2a\u6570\u5b57\u7684\u603b\u548c\u3002<\/li>\n<\/ul>\n<p>\u4f8b\u5982\uff0c\u5728\u4ee5\u4e0b\u77e9\u9635\u4e2d\uff0c\u6211\u4eec\u5c06\u7b2c 2 \u884c\u4e0e\u7b2c 3 \u884c\u76f8\u52a0\u5e76\u4e58\u4ee5 1\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-04417e2094ac05c7a374334c55197f36_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} -1 &amp; -3 &amp; 4 &amp; 1 \\\\[2ex] 2 &amp; 4 &amp; 1 &amp; -5 \\\\[2ex] 1 &amp; -2 &amp; 3 &amp; -1 \\end{array} \\right) \\begin{array}{c}   \\\\[2ex]  \\xrightarrow{f_2 + 1 \\cdot f_3}  \\\\[2ex] &amp; \\end{array} \\left( \\begin{array}{ccc|c} -1 &amp; -3 &amp; 4 &amp; 1 \\\\[2ex] 3 &amp; 2 &amp; 4 &amp; -6 \\\\[2ex] 1 &amp; -2 &amp; 3 &amp; -1 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"98\" width=\"417\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\">\u5982\u4f55\u4f7f\u7528\u9ad8\u65af\u65b9\u6cd5\u6c42\u89e3\u65b9\u7a0b\u7ec4\uff1f<\/h2>\n<p>\u73b0\u5728\u6211\u4eec\u5c06\u901a\u8fc7\u4e00\u4e2a\u4f8b\u5b50\u6765\u4e86\u89e3<strong>\u7528\u9ad8\u65af\u65b9\u6cd5\u6c42\u89e3\u65b9\u7a0b\u7ec4\u7684\u8fc7\u7a0b\uff1a<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-61e6e829301e6730c9e27f9c0a30de2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{r} -x+2y+2z=-24 \\\\[2ex] x+y+z=48 \\\\[2ex] 2x-6y+4z=12 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"179\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u9996\u5148\u8981\u505a\u7684\u662f<strong>\u7cfb\u7edf\u7684\u6269\u5c55\u77e9\u9635<\/strong>\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\/exercice-resolu-de-systeme-dequations-par-la-methode-de-gauss.webp\" alt=\"\u7528\u9ad8\u65af\u65b9\u6cd5\u6c42\u89e3\u7684\u65b9\u7a0b\u7ec4\u793a\u4f8b\" class=\"wp-image-913\" width=\"541\" height=\"175\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u6b63\u5982\u6211\u4eec\u7a0d\u540e\u5c06\u770b\u5230\u7684\uff0c<strong>\u7b2c\u4e00\u884c\u7684\u7b2c\u4e00\u4f4d\u6570\u5b57\u6700\u597d\u662f 1\u3002<\/strong>\u56e0\u6b64\uff0c\u6211\u4eec\u5c06\u66f4\u6539\u7b2c 1 \u884c\u548c\u7b2c 2 \u884c\u7684\u987a\u5e8f\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-b45e0f757ca2880442314f6a4800697b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} -1 &amp; 2 &amp; 2 &amp;-24 \\\\[2ex] 1 &amp; 1 &amp; 1 &amp; 48 \\\\[2ex] 2 &amp; -6 &amp; 4 &amp; 12 \\end{array} \\right)  \\begin{array}{c} \\xrightarrow{ f_1 \\rightarrow f_2} \\\\[2ex] \\xrightarrow{ f_2 \\rightarrow f_1} \\\\[2ex] &amp; \\end{array} \\left( \\begin{array}{ccc|c}   \\color{blue}\\boxed{\\color{black}1} &amp; 1 &amp; 1 &amp; 48 \\\\[2ex] -1 &amp; 2 &amp; 2 &amp;-24 \\\\[2ex] 2 &amp; -6 &amp; 4 &amp; 12  \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"102\" width=\"496\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-background\" style=\"background-color:#dff6ff\">\u9ad8\u65af\u65b9\u6cd5\u7684\u76ee\u6807\u662f\u4f7f<strong>\u4e3b\u5bf9\u89d2\u7ebf\u4ee5\u4e0b\u7684\u6570\u5b57\u4e3a 0<\/strong> \u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u6211\u4eec\u9700\u8981\u5c06\u7ea2\u8272\u6570\u5b57\u8f6c\u6362\u4e3a0\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-28164ac6b48d32c09b4725548c0633f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} 1  &amp; 1 &amp; 1 &amp; 48 \\\\[2ex] \\color{red}\\bm{-1} &amp; 2 &amp; 2 &amp;-24 \\\\[2ex] \\color{red}\\bm{2} &amp; \\color{red}\\bm{-6} &amp; 4 &amp; 12  \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"224\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u4e3a\u4e86\u6d88\u9664\u8fd9\u4e9b\u6570\u5b57\uff0c\u6211\u4eec\u9700\u8981\u5bf9\u884c\u6267\u884c\u9002\u5f53\u7684\u8f6c\u6362\u3002<\/p>\n<div class=\"adsb30\" style=\" margin:px; text-align:\"><\/div>\n<p>\u4f8b\u5982\uff0c\u7b2c\u4e8c\u884c\u7b2c\u4e00\u4e2a\u5143\u7d20 -1 \u662f\u7b2c\u4e00\u884c\u7b2c\u4e00\u4e2a\u5143\u7d20 1 \u7684\u8d1f\u6570\u3002\u56e0\u6b64\uff0c\u5982\u679c<strong>\u6211\u4eec\u5c06\u7b2c\u4e00\u884c\u6dfb\u52a0\u5230\u7b2c\u4e8c\u884c\uff0c<\/strong> -1 \u5c06\u88ab\u6d88\u9664\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-8b22cdc60e02d30a4ed31073c9ad47c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{lccc|c}  &amp; -1  &amp; 2 &amp; 2 &amp; -24  \\\\ + &amp; \\phantom{-}1  &amp; 1 &amp; 1 &amp; \\phantom{-}48   \\\\ \\hline &amp; \\phantom{-}0 &amp; 3 &amp; 3 &amp; \\phantom{-}24  \\end{array} \\begin{array}{l} \\color{blue}\\bm{\\leftarrow f_2} \\\\ \\color{blue}\\bm{\\leftarrow f_1} \\\\ \\phantom{hline} \\\\ \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"68\" width=\"245\" style=\"vertical-align: -29px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u5982\u679c\u6211\u4eec\u8fdb\u884c\u6c42\u548c\uff0c\u6211\u4eec\u6700\u7ec8\u4f1a\u5f97\u5230\u4ee5\u4e0b\u77e9\u9635\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-1b106306b92bfc3e99d602c22d5198bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} 1  &amp; 1 &amp; 1 &amp; 48 \\\\[2ex] -1 &amp; 2 &amp; 2 &amp; -24 \\\\[2ex] 2 &amp; -6 &amp; 4 &amp; 12 \\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; 48 \\\\[2ex]  \\color{blue}\\boxed{\\color{black}0} &amp; 3 &amp; 3 &amp; 24 \\\\[2ex] 2 &amp; -6 &amp; 4 &amp; 12 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"100\" width=\"479\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u8fd9\u6837\u6211\u4eec\u5c31\u6210\u529f\u5730\u5c06-1 \u8f6c\u5316\u4e3a0\u3002<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u8981\u8f6c\u6362 2\u3002\u5982\u679c\u60a8\u6ce8\u610f\u5230\uff0c\u7b2c\u4e09\u884c\u4e2d\u7684\u7b2c\u4e00\u4e2a\u5143\u7d20 2 \u662f\u7b2c\u4e00\u884c\u4e2d\u7684\u7b2c\u4e00\u4e2a\u5143\u7d20 1 \u7684\u4e24\u500d\u3002\u56e0\u6b64\uff0c\u5982\u679c<strong>\u6211\u4eec\u5c06\u7b2c\u4e00\u884c\u4e58\u4ee5 -2 \u6dfb\u52a0\u5230\u7b2c\u4e09\u884c\uff0c\u5219<\/strong>2 \u5c06\u88ab\u6d88\u9664\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-50716b37fe5c1ff45dc2e4b05300e3da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{lccc|c}    &amp;  \\phantom{-}2 &amp; -6 &amp; \\phantom{-}4 &amp; \\phantom{-}12  \\\\ + &amp; -2  &amp; -2 &amp; -2 &amp; -96 \\\\ \\hline &amp;  \\phantom{-}0 &amp; -8 &amp; \\phantom{-}2 &amp; -84  \\end{array} \\begin{array}{l} \\color{blue} \\bm{\\leftarrow f_3} \\\\ \\color{blue} \\bm{\\leftarrow -2 f_1} \\\\ \\phantom{hline} \\\\ \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"68\" width=\"295\" style=\"vertical-align: -29px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u6211\u4eec\u6700\u7ec8\u5f97\u5230\u4ee5\u4e0b\u77e9\u9635\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-36b2fdf8de855cf35049ecefcf7c1da5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} 1  &amp; 1 &amp; 1 &amp; 48 \\\\[2ex]  0 &amp; 3 &amp; 3 &amp; 24 \\\\[2ex] 2 &amp; -6 &amp; 4 &amp; 12 \\end{array} \\right) \\begin{array}{c}   \\\\[2ex]    \\\\[2ex] \\xrightarrow{f_3-2f_1} \\end{array} \\left( \\begin{array}{ccc|c} 1  &amp; 1 &amp; 1 &amp; 48 \\\\[2ex]  0 &amp; 3 &amp; 3 &amp; 24 \\\\[2ex] \\color{blue}\\boxed{\\color{black}0} &amp; -8 &amp; 2 &amp; -84 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"100\" width=\"472\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u8fd9\u6837\u6211\u4eec\u5c31\u6210\u529f\u5730\u5c062\u53d8\u6210\u4e860\u3002<\/p>\n<p>\u6211\u4eec\u73b0\u5728\u8981\u505a\u7684\u5c31\u662f\u5c06 -8 \u8f6c\u6362\u4e3a 0\u3002\u4e3a\u6b64\uff0c<strong>\u6211\u4eec\u5c06\u7b2c\u4e09\u884c\u4e58\u4ee5 3\uff0c\u7136\u540e\u5c06\u7b2c\u4e8c\u884c\u4e58\u4ee5 8\uff1a<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-156b06e383e387edd24cf4be09d98fe9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{lccc|r} &amp; 0  &amp; -24 &amp; \\phantom{2}6 &amp; -252  \\\\ + &amp; 0  &amp; \\phantom{-}24 &amp; 24 &amp; \\phantom{-}192  \\\\ \\hline  &amp; 0 &amp; \\phantom{-2}0 &amp; 30 &amp; -60  \\end{array} \\begin{array}{l}\\color{blue}\\bm{ \\leftarrow 3f_3} \\\\\\color{blue}\\bm{ \\leftarrow 8f_2} \\\\ \\phantom{hline} \\\\ \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"68\" width=\"281\" style=\"vertical-align: -29px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\u6211\u4eec\u5f97\u5230\u4ee5\u4e0b\u77e9\u9635\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-6e2324629222c746a9021ce05ba7d54d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} 1  &amp; 1 &amp; 1 &amp; 48 \\\\[2ex]  0 &amp; 3 &amp; 3 &amp; 24 \\\\[2ex] 0 &amp; -8 &amp; 2 &amp; -84 \\end{array} \\right) \\begin{array}{c}   \\\\[2ex]  \\\\[2ex] \\xrightarrow{3f_3 + 8f_2} \\end{array} \\left( \\begin{array}{ccc|c} 1  &amp; 1 &amp; 1 &amp; 48 \\\\[2ex]  0 &amp; 3 &amp; 3 &amp; 24 \\\\[2ex] 0 &amp; \\color{blue}\\boxed{\\color{black}0} &amp; 30 &amp; -60 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"100\" width=\"488\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u901a\u8fc7\u8fd9\u4e9b\u53d8\u6362\uff0c\u6211\u4eec\u5c06<strong>\u4e3b\u5bf9\u89d2\u7ebf\u4ee5\u4e0b\u7684\u6240\u6709\u6570\u5b57\u90fd\u53d8\u4e3a 0\u3002<\/strong>\u73b0\u5728\u6211\u4eec\u53ef\u4ee5\u6c42\u89e3\u65b9\u7a0b\u7ec4\u4e86\u3002<\/p>\n<p>\u6211\u4eec\u73b0\u5728\u5fc5\u987b<strong>\u5c06\u77e9\u9635\u8f6c\u6362\u4e3a\u5177\u6709\u672a\u77e5\u6570\u7684\u65b9\u7a0b\u7ec4<\/strong>\u3002\u4e3a\u6b64\uff0c\u8bf7\u8bb0\u4f4f\u7b2c\u4e00\u5217\u5bf9\u5e94\u4e8e<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p>\uff0c\u7b2c\u4e8c\u5217<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p>\uff0c\u7b2c\u4e09\u5217<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4586e340cb83d5b642972e97a288fec2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u6700\u540e\u4e00\u5217\u662f\u6ca1\u6709\u672a\u77e5\u6570\u7684\u6570\u5b57\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-6f90de9d9f5a06959a2d4aebf05f4758_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} 1  &amp; 1 &amp; 1 &amp; 48 \\\\[2ex]  0 &amp; 3 &amp; 3 &amp; 24 \\\\[2ex] 0 &amp; 0 &amp; 30 &amp; -60 \\end{array} \\right) \\  \\longrightarrow \\ \\left. \\begin{array}{r} 1x+1y+1z=48 \\\\[2ex] 3y+3z=24 \\\\[2ex] 30z=-60 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"379\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6700\u540e\uff0c\u4e3a\u4e86\u6c42\u89e3\u7cfb\u7edf\uff0c\u6211\u4eec\u9700\u8981<strong>\u81ea\u4e0b\u800c\u4e0a\u6c42\u89e3\u65b9\u7a0b\u7684\u672a\u77e5\u6570\u3002<\/strong>\u7531\u4e8e\u6700\u540e\u4e00\u4e2a\u65b9\u7a0b\u53ea\u6709\u4e00\u4e2a\u672a\u77e5\u6570\uff0c\u6211\u4eec\u53ef\u4ee5\u6c42\u89e3\u5b83\u5e76\u627e\u5230\u5b83\u7684\u503c\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-f609bf44e2a363aca5008fec95c678dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"30z=-60\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"82\" 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-18c467d7caa0bb171c5b1590f9caa694_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z = \\cfrac{-60}{30}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"75\" 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-9881bf11e418247b881ffbb7de1f0565_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{z=-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"55\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u77e5\u9053 z \u662f\u4ec0\u4e48\uff0c\u5982\u679c\u6211\u4eec\u5c06\u5176\u503c\u4ee3\u5165\u7b2c\u4e8c\u4e2a\u65b9\u7a0b\uff0c\u6211\u4eec\u53ef\u4ee5\u627e\u5230<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p>\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-47af5f5709e3e010efe9fb6f9ab0e8c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3y+3z=24 \\ \\xrightarrow{z \\ = \\ -2} \\ 3y+3(-2)=24\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"305\" 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-da13228341b35d3040ae42078cabd99a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3y-6=24\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"90\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8587739ff9abd17db5f6c4c51f4201dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3y=24+6\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"90\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8e6cb4d9575b53c3eafb342482f0dd28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3y=30\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"60\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d5e353e1b4b02441dfcb4258ee4b5480_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\cfrac{30}{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"53\" 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-819c20ffb8ea217c6f5fe196d891beec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y=10}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"51\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u5bf9\u7b2c\u4e00\u4e2a\u65b9\u7a0b\u505a\u540c\u6837\u7684\u4e8b\u60c5\uff1a\u6211\u4eec\u66ff\u6362\u5176\u4ed6\u672a\u77e5\u6570\u7684\u503c\u5e76\u5220\u9664<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p>\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-16197bd2e6cc012ef57ffb9e5dc77e45_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1x+1y+1z=48 \\ \\xrightarrow{y \\ = \\ 10 \\ ; \\ z \\ = \\ -2} \\ 1x+1(10)+1(-2)=48\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"467\" 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-a333e16025e12b5a3220e3673b32cfbc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x+10-2=48\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"122\" 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-11b343d96345b46d6686d9531c5ed39a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=48-10+2\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"121\" 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-5c64ae2e78dc27d215fff9629c45a07d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{x=40}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"52\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\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-edf75d5dd0f035a459aaa69d22286a89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{x=40} \\quad \\bm{y=10} \\quad \\bm{z=-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"192\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-118\"><\/div>\n<\/div>\n<h2 class=\"wp-block-heading\">\u7528\u9ad8\u65af-\u4e54\u4e39\u6cd5\u6c42\u89e3\u65b9\u7a0b\u7ec4\u95ee\u9898<\/h2>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u4f7f\u7528\u9ad8\u65af\u65b9\u6cd5\u6c42\u89e3\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-854043b0e7e3e2166593dcf5c645bfa0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{r} x+y-z=2 \\\\[2ex] x-2y+3z=0 \\\\[2ex] 2x-y+3z=3 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"143\" style=\"vertical-align: 0px;\"><\/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__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" 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\u9996\u5148\u8981\u505a\u7684\u662f\u7cfb\u7edf\u7684\u6269\u5c55\u77e9\u9635\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-1b6369a58b91f31bf4c8bc212ccf68c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{r} x+y-z=2 \\\\[2ex] x-2y+3z=0 \\\\[2ex] 2x-y+3z=3 \\end{array} \\right\\}  \\longrightarrow \\left( \\begin{array}{ccc|c} 1 &amp; 1 &amp; -1 &amp; 2 \\\\[2ex]  1 &amp; -2 &amp; 3 &amp; 0 \\\\[2ex] 2 &amp; -1 &amp; 3 &amp; 3 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"339\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u9700\u8981\u5c06\u4e3b\u6570\u7ec4\u4e0b\u9762\u7684\u6240\u6709\u6570\u5b57\u90fd\u8bbe\u4e3a 0\u3002<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u6211\u4eec\u6267\u884c\u884c\u64cd\u4f5c\u6765\u53d6\u6d88\u7b2c\u4e00\u5217\u7684\u6700\u540e\u4e24\u9879\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-cd42dcf61aebc4c67de13e09dff72f4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c}1 &amp; 1 &amp; -1 &amp; 2 \\\\[2ex]  1 &amp; -2 &amp; 3 &amp; 0 \\\\[2ex] 2 &amp; -1 &amp; 3 &amp; 3 \\end{array} \\right) \\begin{array}{c} \\\\[2ex] \\xrightarrow{f_2 -f_1} \\\\[2ex] \\xrightarrow{f_3-2f_1} &amp; \\end{array} \\left( \\begin{array}{ccc|c} 1 &amp; 1 &amp; -1 &amp; 2 \\\\[2ex]  0 &amp; -3 &amp; 4 &amp; -2  \\\\[2ex] 0 &amp; -3 &amp; 5 &amp; -1 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"98\" width=\"399\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u4ece\u7b2c\u4e8c\u5217\u4e2d\u5220\u9664\u6700\u540e\u4e00\u4e2a\u5143\u7d20\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-13945337848a6f1badf6efe249951124_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c}1 &amp; 1 &amp; -1 &amp; 2 \\\\[2ex]  0 &amp; -3 &amp; 4 &amp; -2 \\\\[2ex] 0 &amp; -3 &amp; 5 &amp; -1 \\end{array} \\right) \\begin{array}{c} \\\\[2ex]  \\\\[2ex] \\xrightarrow{f_3-f_2} &amp; \\end{array} \\left( \\begin{array}{ccc|c} 1 &amp; 1 &amp; -1 &amp; 2 \\\\[2ex] 0 &amp; -3 &amp; 4 &amp; -2 \\\\[2ex] 0 &amp; 0 &amp; 1 &amp; 1 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"98\" width=\"406\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e00\u65e6\u4e3b\u5bf9\u89d2\u7ebf\u4ee5\u4e0b\u7684\u6240\u6709\u6570\u5b57\u90fd\u4e3a 0\uff0c\u6211\u4eec\u73b0\u5728\u5c31\u53ef\u4ee5\u6c42\u89e3\u65b9\u7a0b\u7ec4\u4e86\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u518d\u6b21\u4ee5\u672a\u77e5\u6570\u65b9\u7a0b\u7ec4\u7684\u5f62\u5f0f\u8868\u793a\u77e9\u9635\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-f068c276aae018a668cc005bcad3e641_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} 1 &amp; 1 &amp; -1 &amp; 2 \\\\[2ex] 0 &amp; -3 &amp; 4 &amp; -2 \\\\[2ex] 0 &amp; 0 &amp; 1 &amp; 1 \\end{array} \\right) \\ \\longrightarrow \\ \\left. \\begin{array}{r} x+y-z=2 \\\\[2ex] -3y+4z=-2 \\\\[2ex] 1z=1 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"367\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u4ece\u4e0b\u5230\u4e0a\u6c42\u89e3\u65b9\u7a0b\u7684\u672a\u77e5\u6570\u3002\u6211\u4eec\u9996\u5148\u6c42\u89e3\u6700\u540e\u4e00\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-96b4633173cfb05c06e2c5bdc995d68c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1z= 1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"49\" 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-be8e058ccee5d0aa33ffcce09cd28f98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z=\\bm{1}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"41\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u5c06 z \u7684\u503c\u4ee3\u5165\u7b2c\u4e8c\u4e2a\u65b9\u7a0b\u6765\u6c42 y \u7684\u503c\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-be96e507b80d44350c96abb013cdcaf6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-3y+4z=-2 \\ \\xrightarrow{z \\ = \\ 1} \\ -3y+4(1)=-2\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"316\" 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-8e9d92c48f937b8bffa678a761acee72_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-3y+4=-2\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"107\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-23ff1832dcecc68a83d1e6afdf07a08a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-3y=-2-4\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"108\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-27cf5638a108b52a34c74053b099361e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-3y=-6\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"78\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1c9efb6ee00d7b62fd3f436c1037feb4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\cfrac{-6}{-3} = \\bm{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"97\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u5bf9\u7b2c\u4e00\u4e2a\u65b9\u7a0b\u505a\u540c\u6837\u7684\u4e8b\u60c5\uff1a\u6211\u4eec\u66ff\u6362\u5176\u4ed6\u672a\u77e5\u6570\u7684\u503c\u5e76\u6c42\u89e3 x\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-63f719497b296c95e6e9cf43651598c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x+y-z=2 \\ \\xrightarrow{y \\ = \\ 2 \\ ; \\ z \\ = \\ 1} \\  x+(2)-(1)=2\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"356\" 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-56845b4eb32748e1842b62d558249eb9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x+1=2\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"72\" 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-02e03b55e65a6262280f3d3e592443ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=2-1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"72\" 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-df0486e1bf5773e392faebda4843f515_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{x=1}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\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-3acc67c77d6f5f92d9a684f87a5def90_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{x=1} \\qquad \\bm{y=2} \\qquad \\bm{z=1}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"196\" style=\"vertical-align: -4px;\"><\/p>\n<\/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>\u4f7f\u7528\u9ad8\u65af\u65b9\u6cd5\u6c42\u4ee5\u4e0b\u65b9\u7a0b\u7ec4\u7684\u89e3\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-7d0595899b8137f769c74fce1b21286b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{r} 2x+y+2z=-3 \\\\[2ex] x+3y+2z=5 \\\\[2ex] 4x+2y-z=-1 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"157\" style=\"vertical-align: 0px;\"><\/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__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" 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\u9996\u5148\u8981\u505a\u7684\u662f\u7cfb\u7edf\u7684\u6269\u5c55\u77e9\u9635\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-5e2a16b6d1451520bd8898675c022dc2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{r} 2x+y+2z=-3 \\\\[2ex] x+3y+2z=5 \\\\[2ex] 4x+2y-z=-1 \\end{array} \\right\\}  \\longrightarrow \\left( \\begin{array}{ccc|c} 2 &amp; 1 &amp; 2 &amp; -3 \\\\[2ex] 1 &amp; 3 &amp; 2 &amp; 5 \\\\[2ex] 4 &amp; 2 &amp; -1 &amp; -1 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"352\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8981\u5e94\u7528\u9ad8\u65af\u65b9\u6cd5\uff0c\u5982\u679c\u7b2c\u4e00\u884c\u4e2d\u7684\u7b2c\u4e00\u4e2a\u6570\u5b57\u662f 1 \u4f1a\u66f4\u7b80\u5355\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5c06\u66f4\u6539\u7b2c 1 \u884c\u548c\u7b2c 2 \u884c\u7684\u987a\u5e8f\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-ef7e2e42d0eecb0395afb7c8311b2ade_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c}2 &amp; 1 &amp; 2 &amp; -3 \\\\[2ex] 1 &amp; 3 &amp; 2 &amp; 5 \\\\[2ex] 4 &amp; 2 &amp; -1 &amp; -1 \\end{array} \\right) \\begin{array}{c} \\xrightarrow{f_1\\rightarrow f_2} \\\\[2ex] \\xrightarrow{f_2\\rightarrow f_1} \\\\[2ex] &amp; \\end{array} \\left( \\begin{array}{ccc|c}1 &amp; 3 &amp; 2 &amp; 5 \\\\[2ex] 2 &amp; 1 &amp; 2 &amp; -3 \\\\[2ex]  4 &amp; 2 &amp; -1 &amp; -1\\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"101\" width=\"381\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u9700\u8981\u5c06\u4e3b\u6570\u7ec4\u4e0b\u9762\u7684\u6240\u6709\u6570\u5b57\u90fd\u8bbe\u4e3a 0\u3002<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\u6211\u4eec\u6267\u884c\u884c\u64cd\u4f5c\u6765\u66ff\u6362\u7b2c\u4e00\u5217\u7684\u6700\u540e\u4e24\u4e2a\u5143\u7d20\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-40baaee3bbde9ed1577e00bc1c3b338f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} 1 &amp; 3 &amp; 2 &amp; 5 \\\\[2ex] 2 &amp; 1 &amp; 2 &amp; -3 \\\\[2ex] 4 &amp; 2 &amp; -1 &amp; -1 \\end{array} \\right) \\begin{array}{c} \\\\[2ex] \\xrightarrow{f_2 -2f_1} \\\\[2ex] \\xrightarrow{f_3-4f_1} &amp; \\end{array} \\left( \\begin{array}{ccc|c} 1 &amp; 3 &amp; 2 &amp; 5 \\\\[2ex] 0 &amp; -5 &amp; -2 &amp; -13 \\\\[2ex] 0 &amp; -10 &amp; -9 &amp; -21 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"98\" width=\"417\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u5c06\u7b2c\u4e8c\u5217\u7684\u6700\u540e\u4e00\u4e2a\u5143\u7d20\u8f6c\u6362\u4e3a\u96f6\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-f328906485bfe6ee77833c04869e1240_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c}1 &amp; 3 &amp; 2 &amp; 5 \\\\[2ex] 0 &amp; -5 &amp; -2 &amp; -13 \\\\[2ex] 0 &amp; -10 &amp; -9 &amp; -21\\end{array} \\right) \\begin{array}{c} \\\\[2ex]  \\\\[2ex] \\xrightarrow{f_3-2f_2} &amp; \\end{array} \\left( \\begin{array}{ccc|c} 1 &amp; 3 &amp; 2 &amp; 5 \\\\[2ex] 0 &amp; -5 &amp; -2 &amp; -13 \\\\[2ex]  0 &amp; 0 &amp; -5 &amp; 5 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"98\" width=\"439\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e00\u65e6\u4e3b\u5bf9\u89d2\u7ebf\u4ee5\u4e0b\u7684\u6240\u6709\u6570\u5b57\u90fd\u4e3a 0\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u6c42\u89e3\u65b9\u7a0b\u7ec4\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u518d\u6b21\u4ee5\u672a\u77e5\u6570\u65b9\u7a0b\u7ec4\u7684\u5f62\u5f0f\u8868\u793a\u77e9\u9635\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-a7e129715c720218a5cb25ef07442442_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} 1 &amp; 3 &amp; 2 &amp; 5 \\\\[2ex] 0 &amp; -5 &amp; -2 &amp; -13 \\\\[2ex]  0 &amp; 0 &amp; -5 &amp; 5 \\end{array} \\right) \\ \\longrightarrow \\ \\left. \\begin{array}{r} x+3y+2z=5 \\\\[2ex] -5y-2z=-13 \\\\[2ex] -5z=5 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"384\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u4ece\u4e0b\u5230\u4e0a\u6c42\u89e3\u65b9\u7a0b\u7684\u672a\u77e5\u6570\u3002\u6211\u4eec\u9996\u5148\u6c42\u89e3\u6700\u540e\u4e00\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-a52023bf513299dc6e11f3f0b83478cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-5z= 5\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"62\" 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-8c401bac44e84469a254eca182dbaaf2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z=\\cfrac{5}{-5}=\\bm{-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"103\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u5c06 z \u7684\u503c\u4ee3\u5165\u7b2c\u4e8c\u4e2a\u65b9\u7a0b\u6765\u6c42 y \u7684\u503c\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-802f76b9a10de545be30d16421b0a476_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-5y-2z=-13 \\ \\xrightarrow{z \\ = \\ -1} \\ -5y-2(-1)=-13\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"360\" 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-dba702d28248bdc1928df387178232a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-5y+2=-13\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"117\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-00b2616ea47a24b0c533514cbad0074b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-5y=-13-2\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"116\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7f23dbeb21681cd1e0a85a6e980d578d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-5y=-15\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"86\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-aa2c8d4e1526976ef2450ec835412a4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\cfrac{-15}{-5} = \\bm{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"107\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u5bf9\u7b2c\u4e00\u4e2a\u65b9\u7a0b\u505a\u540c\u6837\u7684\u4e8b\u60c5\uff1a\u6211\u4eec\u66ff\u6362\u5176\u4ed6\u672a\u77e5\u6570\u7684\u503c\u5e76\u6c42\u89e3 x\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-664205a7f0b30720a191edc7ac6b5d4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x+3y+2z=5 \\ \\xrightarrow{y \\ = \\ 3 \\ ; \\ z \\ = \\ -1} \\  x+3(3)+2(-1)=5\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"416\" 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-e08c94f818594a2e81185baa1b81c59e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x+9-2=5\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"103\" 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-9e21aa5a70c92b8a72ef4c9a374d5acf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=5-9+2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"103\" 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-6505a1b32f86c9deb3ab0716f13c3949_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{x=-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\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-1be1c5f4156b37412c9e19a63190d45e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{x=-2} \\qquad \\bm{y=3} \\qquad \\bm{z=-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"224\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-119\"><\/div>\n<\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e603<\/h3>\n<p>\u7528\u9ad8\u65af\u6cd5\u8ba1\u7b97\u4e0b\u5217\u65b9\u7a0b\u7ec4\u7684\u89e3\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-4301eae3179543fbdee7568e8f88aa4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{r} 2x+3y+z=-1 \\\\[2ex] 6x+4y+4z=0 \\\\[2ex] -4x+2y-z=5 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"157\" style=\"vertical-align: 0px;\"><\/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__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" 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\u9996\u5148\u8981\u505a\u7684\u662f\u7cfb\u7edf\u7684\u6269\u5c55\u77e9\u9635\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-c0d96160d6670e817dd39f61816e1e6e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{r} 2x+3y+z=-1 \\\\[2ex] 6x+4y+4z=0 \\\\[2ex] -4x+2y-z=5\\end{array} \\right\\}  \\longrightarrow \\left( \\begin{array}{ccc|c} 2 &amp; 3 &amp; 1 &amp; -1 \\\\[2ex] 6 &amp; 4 &amp; 4 &amp; 0 \\\\[2ex] -4 &amp; 2 &amp; -1 &amp; 5 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"366\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u9700\u8981\u5c06\u7236\u6570\u7ec4\u4e0b\u7684\u6240\u6709\u6570\u5b57\u90fd\u8bbe\u4e3a0\u3002<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\u6211\u4eec\u6267\u884c\u884c\u64cd\u4f5c\u6765\u66ff\u6362\u7b2c\u4e00\u5217\u7684\u6700\u540e\u4e24\u4e2a\u5143\u7d20\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-87853177b6be449178c24e414dc0865a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} 2 &amp; 3 &amp; 1 &amp; -1 \\\\[2ex] 6 &amp; 4 &amp; 4 &amp; 0 \\\\[2ex] -4 &amp; 2 &amp; -1 &amp; 5\\end{array} \\right) \\begin{array}{c} \\\\[2ex] \\xrightarrow{f_2 -3f_1} \\\\[2ex] \\xrightarrow{f_3+2f_1} &amp; \\end{array} \\left( \\begin{array}{ccc|c} 2 &amp; 3 &amp; 1 &amp; -1 \\\\[2ex] 0 &amp; -5 &amp; 1 &amp; 3 \\\\[2ex] 0 &amp; 8 &amp; 1 &amp; 3\\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"98\" width=\"399\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u5c06\u7b2c\u4e8c\u5217\u7684\u6700\u540e\u4e00\u4e2a\u5143\u7d20\u8f6c\u6362\u4e3a\u96f6\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-c4105ceb64b201c532109f8639bdefde_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c}2 &amp; 3 &amp; 1 &amp; -1 \\\\[2ex] 0 &amp; -5 &amp; 1 &amp; 3 \\\\[2ex] 0 &amp; 8 &amp; 1 &amp; 3\\end{array} \\right) \\begin{array}{c} \\\\[2ex]  \\\\[2ex] \\xrightarrow{5f_3+8f_2} &amp; \\end{array} \\left( \\begin{array}{ccc|c} 2 &amp; 3 &amp; 1 &amp; -1 \\\\[2ex] 0 &amp; -5 &amp; 1 &amp; 3 \\\\[2ex] 0 &amp; 0 &amp; 13 &amp; 39 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"98\" width=\"401\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e00\u65e6\u4e3b\u5bf9\u89d2\u7ebf\u4ee5\u4e0b\u7684\u6240\u6709\u6570\u5b57\u90fd\u4e3a 0\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u6c42\u89e3\u65b9\u7a0b\u7ec4\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u518d\u6b21\u4ee5\u672a\u77e5\u6570\u65b9\u7a0b\u7ec4\u7684\u5f62\u5f0f\u8868\u793a\u77e9\u9635\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-faae83295a3f7b3d8b6d76f78d56fac6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} 2 &amp; 3 &amp; 1 &amp; -1 \\\\[2ex] 0 &amp; -5 &amp; 1 &amp; 3 \\\\[2ex] 0 &amp; 0 &amp; 13 &amp; 39\\end{array} \\right) \\ \\longrightarrow \\ \\left. \\begin{array}{r} 2x+3y+1z=-1 \\\\[2ex] -5y+z=3 \\\\[2ex] 13z=39 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"389\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u4ece\u4e0b\u5230\u4e0a\u6c42\u89e3\u65b9\u7a0b\u7684\u672a\u77e5\u6570\u3002\u6211\u4eec\u9996\u5148\u6c42\u89e3\u6700\u540e\u4e00\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-4ce4c9f218fa1bd1448e77039773f7d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"13z= 39\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"67\" 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-2b17181241c9203cad7e9e776a3e4fbe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z=\\cfrac{39}{13}=\\bm{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"85\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u5c06 z \u7684\u503c\u4ee3\u5165\u7b2c\u4e8c\u4e2a\u65b9\u7a0b\u6765\u6c42 y \u7684\u503c\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-60d5784aa102e6db8696ba9bf79e1da5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-5y+z=3 \\ \\xrightarrow{z \\ = \\ 3} \\ -5y+(3)=3\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"272\" 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-48fbd56cf56ffcfb7d9c676eecf02550_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-5y=3-3\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"94\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8ee955981979845afcdca2dfbefe7fca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-5y=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"64\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-720b6716d584d822d06446bcc18382e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\cfrac{0}{-5} = \\bm{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"90\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u5bf9\u7b2c\u4e00\u4e2a\u65b9\u7a0b\u505a\u540c\u6837\u7684\u4e8b\u60c5\uff1a\u6211\u4eec\u66ff\u6362\u5176\u4ed6\u672a\u77e5\u6570\u7684\u503c\u5e76\u6c42\u89e3 x\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-ed92c6b5eec53094b5ff47ff6274f113_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x+3y+1z=-1 \\ \\xrightarrow{y \\ = \\ 0 \\ ; \\ z \\ = \\ 3} \\  2x+3(0)+1(3)=-1\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"437\" 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-d7df18713df47399b523eb5025194be6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x+0+3=-1\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"126\" 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-994c82dc1b5d22d408db4477e0964fec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x=-1-3\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"96\" 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-8bb8c1283df065c83c44b7fe484324a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x=-4\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"66\" 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-d9dd0f99977b1208f94006aaa348d060_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\cfrac{-4}{2}=\\bm{-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"112\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\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-93fd2b17430c25b9d44e5afc2e099e0f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{x=-2} \\qquad \\bm{y=0} \\qquad \\bm{z=3}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"211\" style=\"vertical-align: -4px;\"><\/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>\u4f7f\u7528\u9ad8\u65af\u65b9\u6cd5\u6c42\u89e3\u4ee5\u4e0b\u5177\u6709 3 \u4e2a\u672a\u77e5\u6570\u7684\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-b005b2eda0d63c7130f2f5531c2ae4a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{r}  2x-6=4y+6z \\\\[2ex] -y-3z=1-3x \\\\[2ex] -4x-y=6-3z \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"156\" style=\"vertical-align: 0px;\"><\/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__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" 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\">\u5728\u5e94\u7528\u9ad8\u65af\u65b9\u6cd5\u4e4b\u524d\uff0c\u6211\u4eec\u9700\u8981\u6392\u5217\u65b9\u7a0b\u7ec4\uff0c\u4f7f\u6240\u6709\u672a\u77e5\u6570\u4f4d\u4e8e\u65b9\u7a0b\u5de6\u4fa7\uff0c\u6570\u5b57\u4f4d\u4e8e\u53f3\u4fa7\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-1e0ca77b625e8f9e235ce8da4e4008df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{r}2x-6=4y+6z \\\\[2ex] -y-3z=1-3x \\\\[2ex] -4x-y=6-3z \\end{array} \\right\\} \\longrightarrow \\left.  \\begin{array}{r} 2x-4y-6z=6 \\\\[2ex] 3x-y-3z=1 \\\\[2ex] -4x-y+3z=6\\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"364\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e00\u65e6\u7cfb\u7edf\u88ab\u8ba2\u8d2d\uff0c\u6211\u4eec\u5c31\u6784\u5efa\u7cfb\u7edf\u7684\u5f00\u53d1\u77e9\u9635\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-b88e3ff141b847028a55ba4b46b8e870_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{r} 2x-4y-6z=6 \\\\[2ex] 3x-y-3z=1 \\\\[2ex] -4x-y+3z=6 \\end{array} \\right\\}  \\longrightarrow \\left( \\begin{array}{ccc|c} 2 &amp; -4 &amp; -6 &amp; 6 \\\\[2ex] 3 &amp; -1 &amp; -3 &amp; 1 \\\\[2ex] -4 &amp; -1 &amp; 3 &amp; 6 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"365\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7531\u4e8e\u7b2c\u4e00\u884c\u4e2d\u7684\u6240\u6709\u6570\u5b57\u90fd\u662f\u5076\u6570\uff0c\u56e0\u6b64\u5728\u5bf9\u884c\u8fdb\u884c\u64cd\u4f5c\u4e4b\u524d\uff0c\u6211\u4eec\u5c06\u7b2c\u4e00\u884c\u9664\u4ee5 2\u3002\u56e0\u4e3a\u8fd9\u5c06\u4f7f\u8ba1\u7b97\u66f4\u5bb9\u6613\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-b05235526cd8e44c16749606bfe8976c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c}2 &amp; -4 &amp; -6 &amp; 6 \\\\[2ex] 3 &amp; -1 &amp; -3 &amp; 1 \\\\[2ex] -4 &amp; -1 &amp; 3 &amp; 6 \\end{array} \\right) \\begin{array}{c} \\xrightarrow{f_1\/2} \\\\[2ex] \\\\[2ex] &amp; \\end{array} \\left( \\begin{array}{ccc|c}1 &amp; -2 &amp; -3 &amp; 3 \\\\[2ex] 3 &amp; -1 &amp; -3 &amp; 1 \\\\[2ex] -4 &amp; -1 &amp; 3 &amp; 6\\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"99\" width=\"396\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u9700\u8981\u5c06\u4e3b\u6570\u7ec4\u4e0b\u9762\u7684\u6240\u6709\u6570\u5b57\u90fd\u8bbe\u4e3a 0\u3002<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\u6211\u4eec\u6267\u884c\u884c\u64cd\u4f5c\u6765\u66ff\u6362\u7b2c\u4e00\u5217\u7684\u6700\u540e\u4e24\u4e2a\u5143\u7d20\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-3da82815d14fdfae0f61a8e1747fb9fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} 1 &amp; -2 &amp; -3 &amp; 3 \\\\[2ex] 3 &amp; -1 &amp; -3 &amp; 1 \\\\[2ex] -4 &amp; -1 &amp; 3 &amp; 6 \\end{array} \\right) \\begin{array}{c} \\\\[2ex] \\xrightarrow{f_2 -3f_1} \\\\[2ex] \\xrightarrow{f_3+4f_1} &amp; \\end{array} \\left( \\begin{array}{ccc|c} 1 &amp; -2 &amp; -3 &amp; 3 \\\\[2ex] 0 &amp; 5 &amp; 6 &amp; -8 \\\\[2ex] 0 &amp; -9 &amp; -9 &amp; 18\\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"98\" width=\"413\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u548c\u4e4b\u524d\u4e00\u6837\uff0c\u7531\u4e8e\u6700\u540e\u4e00\u884c\u4e2d\u7684\u6240\u6709\u6570\u5b57\u90fd\u662f 9 \u7684\u500d\u6570\uff0c\u56e0\u6b64\u6211\u4eec\u5c06\u5176\u9664\u4ee5 9 \u4ee5\u4f7f\u8ba1\u7b97\u66f4\u5bb9\u6613\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-342000d19a7bd19e055a39695c79cb49_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c}1 &amp; -2 &amp; -3 &amp; 3 \\\\[2ex] 0 &amp; 5 &amp; 6 &amp; -8 \\\\[2ex] 0 &amp; -9 &amp; -9 &amp; 18 \\end{array} \\right) \\begin{array}{c}  \\\\[2ex] \\\\[2ex]\\xrightarrow{f_3\/9} &amp; \\end{array} \\left( \\begin{array}{ccc|c}1 &amp; -2 &amp; -3 &amp; 3 \\\\[2ex] 0 &amp; 5 &amp; 6 &amp; -8 \\\\[2ex] 0 &amp; -1 &amp; -1 &amp; 2\\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"396\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u5c06\u7b2c\u4e8c\u5217\u7684\u6700\u540e\u4e00\u4e2a\u5143\u7d20\u8f6c\u6362\u4e3a\u96f6\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-2158e7f439f677617bb8a40695fb5711_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c}1 &amp; -2 &amp; -3 &amp; 3 \\\\[2ex] 0 &amp; 5 &amp; 6 &amp; -8 \\\\[2ex] 0 &amp; -1 &amp; -1 &amp; 2\\end{array} \\right) \\begin{array}{c} \\\\[2ex]  \\\\[2ex] \\xrightarrow{5f_3+f_2} &amp; \\end{array} \\left( \\begin{array}{ccc|c} 1 &amp; -2 &amp; -3 &amp; 3 \\\\[2ex] 0 &amp; 5 &amp; 6 &amp; -8 \\\\[2ex] 0 &amp; 0 &amp; 1 &amp; 2 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"98\" width=\"413\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e00\u65e6\u4e3b\u5bf9\u89d2\u7ebf\u4ee5\u4e0b\u7684\u6240\u6709\u6570\u5b57\u90fd\u4e3a 0\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u6c42\u89e3\u65b9\u7a0b\u7ec4\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u518d\u6b21\u4ee5\u672a\u77e5\u6570\u65b9\u7a0b\u7ec4\u7684\u5f62\u5f0f\u8868\u793a\u77e9\u9635\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-ea162e98aa70f8d56ffba28438a9de2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{array}{ccc|c} 1 &amp; -2 &amp; -3 &amp; 3 \\\\[2ex] 0 &amp; 5 &amp; 6 &amp; -8 \\\\[2ex] 0 &amp; 0 &amp; 1 &amp; 2 \\end{array} \\right) \\ \\longrightarrow \\ \\left. \\begin{array}{r} x-2y-3z=3 \\\\[2ex] 5y+6z=-8 \\\\[2ex] 1z=2 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"371\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u4ece\u4e0b\u5230\u4e0a\u6c42\u89e3\u65b9\u7a0b\u7684\u672a\u77e5\u6570\u3002\u6211\u4eec\u9996\u5148\u6c42\u89e3\u6700\u540e\u4e00\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-28e1aa243598bedb00978eb5e0c1dcd3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1z= 2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"49\" 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-4307991ada04e86ea4085fe426ea9f08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z=\\bm{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"41\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u5c06 z \u7684\u503c\u4ee3\u5165\u7b2c\u4e8c\u4e2a\u65b9\u7a0b\u6765\u6c42 y \u7684\u503c\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-b5eb143e26fb1f1535d4c2596c889007_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"5y+6z=-8 \\ \\xrightarrow{z \\ = \\ 2} \\ 5y+6(2)=-8\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"291\" 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-48b6461c0e3832049edb903a568752df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"5y+12=-8\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"104\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4c9094946053033193fa68d290041f3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"5y=-8-12\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"103\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8492d7042878af6f3863f5e83213a2ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"5y=-20\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"74\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fe3119924b2e0ee7a98cc5489223e689_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\cfrac{-20}{5} = \\bm{-4}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"121\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u5bf9\u7b2c\u4e00\u4e2a\u65b9\u7a0b\u505a\u540c\u6837\u7684\u4e8b\u60c5\uff1a\u6211\u4eec\u66ff\u6362\u5176\u4ed6\u672a\u77e5\u6570\u7684\u503c\u5e76\u6c42\u89e3 x\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-d3e3bbe943253ea68f811850c1b882bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x-2y-3z=3 \\ \\xrightarrow{y \\ = \\ -4 \\ ; \\ z \\ = \\ 2} \\  x-2(-4)-3(2)=3\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"417\" 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-b5d555ad593794ad6d247dbbc2cd98eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x+8-6=3\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"104\" 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-af64e62e2b2b22939ce0f08900f91404_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=3-8+6\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"104\" 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-df0486e1bf5773e392faebda4843f515_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{x=1}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\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-586cec7145ab5b293cadaafd4f7bb738_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{x=-1} \\qquad \\bm{y=-4} \\qquad \\bm{z=2}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"224\" style=\"vertical-align: -4px;\"><\/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\u4e86\u89e3\u4ec0\u4e48\u662f Gauss-Jordan \u65b9\u6cd5\u4ee5\u53ca\u5982\u4f55\u4f7f\u7528\u9ad8\u65af\u65b9\u6cd5\u6c42\u89e3\u65b9\u7a0b\u7ec4\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u5c06\u627e\u5230\u4f7f\u7528 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e4%b9%94%e4%b8%b9%e9%ab%98%e6%96%af%e6%96%b9%e6%b3%95%e5%8f%8a%e5%85%b6%e7%a4%ba%e4%be%8b%e5%92%8c%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%9a%84%e7%bb%83%e4%b9%a0\/\"> <span class=\"screen-reader-text\">\u9ad8\u65af\u65b9\u6cd5\u2014\u2014\u4e54\u4e39<\/span> \u67e5\u770b\u5168\u6587 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