{"id":298,"date":"2023-07-06T14:13:39","date_gmt":"2023-07-06T14:13:39","guid":{"rendered":"https:\/\/mathority.org\/cn\/cramer-%e7%9a%84%e8%a7%84%e5%88%99%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":"2023-07-06T14:13:39","modified_gmt":"2023-07-06T14:13:39","slug":"cramer-%e7%9a%84%e8%a7%84%e5%88%99%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\/cramer-%e7%9a%84%e8%a7%84%e5%88%99%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":"\u514b\u83b1\u9ed8\u6cd5\u5219"},"content":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u4e86\u89e3\u4ec0\u4e48\u662f\u514b\u83b1\u9ed8\u89c4\u5219\uff0c\u6b64\u5916\uff0c\u60a8\u8fd8\u5c06\u627e\u5230\u901a\u8fc7\u514b\u83b1\u9ed8\u89c4\u5219\u6c42\u89e3\u65b9\u7a0b\u7ec4\u7684\u793a\u4f8b\u548c\u7ec3\u4e60\u3002<\/p>\n<h2 class=\"wp-block-heading\">\u4ec0\u4e48\u662f\u514b\u83b1\u9ed8\u6cd5\u5219\uff1f<\/h2>\n<p><strong>\u514b\u83b1\u9ed8\u6cd5\u5219<\/strong>\u662f\u4e00\u79cd\u7528\u4e8e\u901a\u8fc7\u884c\u5217\u5f0f\u6c42\u89e3\u65b9\u7a0b\u7ec4\u7684\u65b9\u6cd5\u3002\u6211\u4eec\u6765\u770b\u770b\u5b83\u662f\u5982\u4f55\u4f7f\u7528\u7684\uff1a<\/p>\n<p>\u8003\u8651\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-e0141f3451719f665ef28e4061489551_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases} ax+by+cz= \\color{red}\\bm{j} \\\\[1.5ex] dx+ey+fz=\\color{red}\\bm{k} \\\\[1.5ex] gx+hy+iz = \\color{red}\\bm{l} \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"171\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u7cfb\u7edf\u7684\u77e9\u9635A\u548c\u6269\u5c55\u77e9\u9635A&#8217;\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-1d628a13ec7de4b3ba7a301c0a5d8ac6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A= \\left( \\begin{array}{ccc} a &amp; b &amp; c  \\\\[1.1ex] d &amp; e &amp; f  \\\\[1.1ex] g &amp; h &amp; i  \\end{array} \\right) \\qquad A'= \\left( \\begin{array}{ccc|c} a &amp; b &amp; c &amp;  \\color{red}\\bm{j}  \\\\[1.1ex] d &amp; e &amp; f &amp; \\color{red}\\bm{k} \\\\[1.1ex] g &amp; h &amp; i &amp; \\color{red}\\bm{l} \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"384\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p><strong><span style=\"text-decoration: underline;\">\u514b\u83b1\u9ed8\u6cd5\u5219<\/span><\/strong>\u6307\u51fa\u65b9\u7a0b\u7ec4\u7684\u89e3\u4e3a\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/quelle-est-la-regle-de-cramer.webp\" alt=\"\u4ec0\u4e48\u662f\u514b\u62c9\u9ed8\u6cd5\u5219\uff0c\u514b\u62c9\u9ed8\u6cd5\u5219\u89e3\u91ca\" class=\"wp-image-1062\" width=\"677\" height=\"385\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u8bf7\u6ce8\u610f\uff0c\u5206\u5b50\u7684\u884c\u5217\u5f0f\u7c7b\u4f3c\u4e8e\u77e9\u9635 A \u7684\u884c\u5217\u5f0f\uff0c\u4f46\u5c06\u6bcf\u4e2a\u672a\u77e5\u6570\u7684\u5217\u66f4\u6539\u4e3a\u72ec\u7acb\u9879\u7684\u5217\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u514b\u83b1\u9ed8\u6cd5\u5219\u7528\u4e8e\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u3002\u4f46\u662f\uff0c\u6b63\u5982\u60a8\u6240\u77e5\uff0c\u6c42\u89e3\u65b9\u7a0b\u7ec4\u7684\u65b9\u6cd5\u6709\u5f88\u591a\uff0c\u4f8b\u5982\u4f17\u6240\u5468\u77e5\u7684<a href=\"https:\/\/mathority.org\/cn\/\u4e54\u4e39\u9ad8\u65af\u65b9\u6cd5\u53ca\u5176\u793a\u4f8b\u548c\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\/\">\u9ad8\u65af\u4e54\u4e39\u65b9\u6cd5<\/a>\u3002<\/p>\n<p>\u4ee5\u4e0b\u662f\u4f7f\u7528\u514b\u83b1\u9ed8\u6cd5\u5219\uff08\u6709\u65f6\u4e5f\u5199\u4e3a\u514b\u83b1\u9ed8\u6cd5\u5219\uff09\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u793a\u4f8b\u3002<\/p>\n<h2 class=\"wp-block-heading\">\u793a\u4f8b1\uff1a\u786e\u5b9a\u517c\u5bb9\u7cfb\u7edf\uff08SCD\uff09<\/h2>\n<ul>\n<li>\u4f7f\u7528\u514b\u83b1\u9ed8\u6cd5\u5219\u6c42\u89e3\u4ee5\u4e0b\u5177\u6709 3 \u4e2a\u672a\u77e5\u6570\u7684 3 \u4e2a\u65b9\u7a0b\u7ec4\uff1a<\/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-6013b7e73c89c24fe388f1a5d018f32b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases} 2x+y+3z= 1 \\\\[1.5ex] 3x-2y-z=0 \\\\[1.5ex] x+3y+2z = 5\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"135\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u9996\u5148\u5236\u4f5c\u7cfb\u7edf\u7684\u77e9\u9635A\u548c\u6269\u5c55\u77e9\u9635A&#8217;\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-c710ed86223f47f39b5a25720b5ca19d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A= \\left( \\begin{array}{ccc} 2 &amp; 1 &amp; 3 \\\\[1.1ex] 3 &amp; -2 &amp; -1 \\\\[1.1ex] 1 &amp; 3 &amp; 2\\end{array} \\right) \\qquad A'= \\left( \\begin{array}{ccc|c} 2 &amp; 1 &amp; 3 &amp; 1 \\\\[1.1ex] 3 &amp; -2 &amp; -1 &amp; 0 \\\\[1.1ex] 1 &amp; 3 &amp; 2 &amp; 5 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"405\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u8ba1\u7b97\u4e24\u4e2a\u77e9\u9635\u7684\u79e9\uff0c\u4ee5\u4e86\u89e3\u5b83\u662f\u4ec0\u4e48\u7c7b\u578b\u7684\u7cfb\u7edf\u3002\u4e3a\u4e86\u8ba1\u7b97 A \u7684\u79e9\uff0c\u6211\u4eec\u8ba1\u7b97\u6574\u4e2a\u77e9\u9635\u7684 3\u00d73 \u884c\u5217\u5f0f\uff08\u4f7f\u7528 Sarrus \u89c4\u5219\uff09\u5e76\u67e5\u770b\u5b83\u662f\u5426\u7ed9\u51fa 0\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-ae4a3bb88d113494463df8e670c326c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix}A \\end{vmatrix}= \\begin{vmatrix} 2 &amp; 1 &amp; 3 \\\\[1.1ex] 3 &amp; -2 &amp; -1 \\\\[1.1ex] 1 &amp; 3 &amp; 2\\end{vmatrix} =-8-1+27+6+6-6 = 24 \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"427\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> A \u7684\u884c\u5217\u5f0f\u4e0d\u4e3a 0\uff0c\u56e0\u6b64<strong>\u77e9\u9635 A \u7684\u79e9\u4e3a 3\u3002<\/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-842ae3b68df41813d9e409968f3ae946_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  rg(A)=3\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"77\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c<strong>\u77e9\u9635 A&#8217; \u7684\u79e9\u4e5f\u662f 3<\/strong> \uff0c\u56e0\u4e3a\u5b83\u4e0d\u80fd\u662f\u79e9 4 \u5e76\u4e14\u5fc5\u987b\u81f3\u5c11\u4e0e\u77e9\u9635 A \u5177\u6709\u76f8\u540c\u7684\u79e9\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-150bbc9c8e363db471c2d5bc4f33e1fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  rg(A')=3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"82\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u77e9\u9635 A \u7684\u8303\u56f4\u7b49\u4e8e\u77e9\u9635 A&#8217; \u7684\u8303\u56f4\u548c\u7cfb\u7edf (3) \u7684\u672a\u77e5\u6570\u4e2a\u6570\uff0c\u56e0\u6b64\uff0c\u6839\u636e<strong>Rouch\u00e9-Frobenius \u5b9a\u7406<\/strong>\uff0c\u6211\u4eec\u77e5\u9053\u5b83\u662f\u4e00\u4e2a<strong>\u786e\u5b9a\u7684\u517c\u5bb9\u7cfb\u7edf<\/strong>\uff08SCD\uff09\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-557185e16670c72d23eec5a3ea13b487_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{array}{c} \\begin{array}{c} \\color{black}rg(A) = 3 \\\\[1.3ex] \\color{black}rg(A')=3 \\\\[1.3ex] \\color{black}\\text{N\\'umero de inc\\'ognitas} = 3    \\end{array}} \\\\ \\\\  \\color{blue} \\boxed{ \\color{black}\\phantom{^9_9} rg(A) = rg(A') = n = 3  \\color{blue} \\ \\bm{\\longrightarrow} \\ \\color{black} \\bm{SCD}\\phantom{^9_9}} \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"138\" width=\"436\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u4e00\u65e6\u6211\u4eec\u77e5\u9053\u7cfb\u7edf\u662f\u4e00\u4e2a SCD\uff0c\u6211\u4eec\u5c31\u5e94\u7528<strong>\u514b\u83b1\u9ed8\u89c4\u5219<\/strong>\u6765\u89e3\u51b3\u5b83\u3002\u4e3a\u6b64\uff0c\u8bf7\u56de\u60f3\u4e00\u4e0b\u77e9\u9635 A\u3001\u5176\u884c\u5217\u5f0f\u548c\u77e9\u9635 A&#8217; \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-31b2b3e5865c2264c360fb887d37a5f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A= \\left( \\begin{array}{ccc} 2 &amp; 1 &amp; 3 \\\\[1.1ex] 3 &amp; -2 &amp; -1 \\\\[1.1ex] 1 &amp; 3 &amp; 2\\end{array} \\right) \\qquad A'= \\left( \\begin{array}{ccc|c} 2 &amp; 1 &amp; 3 &amp; \\color{red}\\bm{1} \\\\[1.1ex] 3 &amp; -2 &amp; -1 &amp; \\color{red}\\bm{0} \\\\[1.1ex] 1 &amp; 3 &amp; 2 &amp; \\color{red}\\bm{5} \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"431\" 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-0a604d8f5a3927a47a264d28f7a007b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix}A \\end{vmatrix}= \\begin{vmatrix} 2 &amp; 1 &amp; 3 \\\\[1.1ex] 3 &amp; -2 &amp; -1 \\\\[1.1ex] 1 &amp; 3 &amp; 2\\end{vmatrix} =24\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"187\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u8ba1\u7b97\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-757d0eed520b26d08cc3b8b397d0f980_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u6839\u636e\u514b\u83b1\u9ed8\u89c4\u5219\uff0c\u6211\u4eec\u5c06 A \u884c\u5217\u5f0f\u7684\u7b2c\u4e00\u5217\u66f4\u6539\u4e3a\u72ec\u7acb\u9879\u5217\uff0c\u7136\u540e\u5c06\u5176\u9664\u4ee5 A \u7684\u884c\u5217\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-a1fa494ffb5e452d59c4d2dad40f925a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{x} = \\cfrac{\\begin{vmatrix} \\color{red}\\bm{1} &amp; 1 &amp; 3 \\\\[1.1ex] \\color{red}\\bm{0} &amp; -2 &amp; -1 \\\\[1.1ex] \\color{red}\\bm{5} &amp; 3 &amp; 2 \\end{vmatrix}}{\\begin{vmatrix} A \\end{vmatrix}} = \\cfrac{24}{24} = \\bm{1}\" title=\"Rendered by QuickLaTeX.com\" height=\"113\" width=\"238\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u8ba1\u7b97\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-5fb4fb8b1addff607711094fd1ed326e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u6839\u636e\u514b\u83b1\u9ed8\u89c4\u5219\uff0c\u6211\u4eec\u5c06 A \u884c\u5217\u5f0f\u7684\u7b2c\u4e8c\u5217\u66f4\u6539\u4e3a\u72ec\u7acb\u9879\u5217\uff0c\u5e76\u5c06\u5176\u9664\u4ee5 A \u7684\u884c\u5217\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-08e3dabe2f33434eb96658491f67c0b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{y} = \\cfrac{\\begin{vmatrix} 2 &amp; \\color{red}\\bm{1} &amp; 3 \\\\[1.1ex] 3 &amp;  \\color{red}\\bm{0} &amp; -1 \\\\[1.1ex] 1 &amp; \\color{red}\\bm{5} &amp; 2\\end{vmatrix}}{\\begin{vmatrix} A \\end{vmatrix}} = \\cfrac{48}{24} = \\bm{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"113\" width=\"223\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u8ba1\u7b97<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-23aa090e6102a41de5ad5515112e4d03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  z\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u6839\u636e\u514b\u83b1\u9ed8\u89c4\u5219\uff0c\u6211\u4eec\u5c06 A \u884c\u5217\u5f0f\u7684\u7b2c\u4e09\u5217\u66f4\u6539\u4e3a\u72ec\u7acb\u9879\u5217\uff0c\u5e76\u5c06\u5176\u9664\u4ee5 A \u7684\u884c\u5217\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-96e76cb8867224755e9c19254678abd4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{z} = \\cfrac{\\begin{vmatrix} 2 &amp; 1 &amp; \\color{red}\\bm{1} \\\\[1.1ex] 3 &amp; -2 &amp;  \\color{red}\\bm{0} \\\\[1.1ex] 1 &amp; 3 &amp;  \\color{red}\\bm{5}\\end{vmatrix}}{\\begin{vmatrix} A \\end{vmatrix}} = \\cfrac{-24}{24} = \\bm{-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"113\" width=\"259\" 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-be5a19fed42dcb59880c2d0eee8e51f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{x = 1 \\qquad y=2 \\qquad z = -1}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"210\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\">\u793a\u4f8b 2\uff1a\u4e0d\u786e\u5b9a\u517c\u5bb9\u7cfb\u7edf (ICS)<\/h2>\n<ul>\n<li>\u4f7f\u7528\u514b\u83b1\u9ed8\u6cd5\u5219\u6c42\u89e3\u4ee5\u4e0b\u65b9\u7a0b\u7ec4\uff1a<\/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-781530aac4d8507fd6c7cbd77c3b4651_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases} 3x+2y+4z=1 \\\\[1.5ex] -2x+3y-z=0 \\\\[1.5ex] x+5y+3z = 1 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"149\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u9996\u5148\u5236\u4f5c\u7cfb\u7edf\u7684\u77e9\u9635A\u548c\u6269\u5c55\u77e9\u9635A&#8217;\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-a64800a78bf8e2e2f547be907e6863cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A= \\left( \\begin{array}{ccc} 3 &amp; 2 &amp; 4 \\\\[1.1ex] -2 &amp; 3 &amp; -1 \\\\[1.1ex] 1 &amp; 5 &amp; 3 \\end{array} \\right) \\qquad A'= \\left( \\begin{array}{ccc|c} 3 &amp; 2 &amp; 4 &amp; 1 \\\\[1.1ex] -2 &amp; 3 &amp; -1 &amp; 0 \\\\[1.1ex] 1 &amp; 5 &amp; 3 &amp; 1 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"405\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u8ba1\u7b97\u4e24\u4e2a\u77e9\u9635\u7684\u8303\u56f4\uff0c\u4ece\u800c\u53ef\u4ee5\u770b\u51fa\u5b83\u662f\u4ec0\u4e48\u7c7b\u578b\u7684\u7cfb\u7edf\u3002\u4e3a\u4e86\u8ba1\u7b97 A \u7684\u79e9\uff0c\u6211\u4eec\u8ba1\u7b97\u6574\u4e2a\u77e9\u9635\u7684\u884c\u5217\u5f0f\uff08\u4f7f\u7528 Sarrus \u89c4\u5219\uff09\u5e76\u68c0\u67e5\u5b83\u662f\u5426\u4e3a 0\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-581c58cbe0fdd9952e7e25b919ecc33b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix}A \\end{vmatrix}= \\begin{vmatrix} 3 &amp; 2 &amp; 4 \\\\[1.1ex] -2 &amp; 3 &amp; -1 \\\\[1.1ex] 1 &amp; 5 &amp; 3\\end{vmatrix} = 27-2-40-12+15+12= 0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"407\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u884c\u5217\u5f0f\u7ed9\u51fa 0\uff0c\u56e0\u6b64\u77e9\u9635 A \u7684\u79e9\u4e0d\u662f 3\u3002\u4f46\u5b83\u6709\u4e00\u4e2a\u4e0d\u540c\u4e8e 0 \u7684 2\u00d72 \u884c\u5217\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-a5d1acad8bc31240f80d8cfbf3605997_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} 3 &amp; 2 \\\\[1.1ex] -2 &amp; 3 \\end{vmatrix} =9-(-4)=13\\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"222\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6240\u4ee5<strong>\u77e9\u9635 A \u7684\u79e9\u4e3a 2<\/strong> \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-eded270b78ab3d95ce827e3ea428efb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  rg(A)=2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"76\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4e00\u65e6\u6211\u4eec\u77e5\u9053\u4e86\u77e9\u9635 A \u7684\u8303\u56f4\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u8ba1\u7b97\u77e9\u9635 A&#8217; \u7684\u8303\u56f4\u3002\u524d 3 \u5217\u7684\u884c\u5217\u5f0f\u7ed9\u51fa 0\uff0c\u56e0\u6b64\u6211\u4eec\u5c1d\u8bd5\u77e9\u9635 A&#8217; \u4e2d\u5176\u4ed6\u53ef\u80fd\u7684 3\u00d73 \u884c\u5217\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-686e7ca635ecee685005f6013c2e64ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} 2 &amp; 4 &amp; 1 \\\\[1.1ex] 3 &amp; -1 &amp; 0 \\\\[1.1ex] 5 &amp; 3 &amp; 1 \\end{vmatrix} = 0 \\qquad \\begin{vmatrix} 3 &amp; 4 &amp; 1 \\\\[1.1ex] -2 &amp; -1 &amp; 0 \\\\[1.1ex] 1 &amp; 3 &amp; 1 \\end{vmatrix} = 0 \\qquad \\begin{vmatrix} 3 &amp; 2 &amp; 1 \\\\[1.1ex] -2 &amp; 3 &amp; 0 \\\\[1.1ex] 1 &amp; 5 &amp; 1 \\end{vmatrix} = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"440\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6240\u6709 3 \u9636\u884c\u5217\u5f0f\u90fd\u7ed9\u51fa 0\u3002\u4f46\u662f\uff0c\u663e\u7136\uff0c\u77e9\u9635 A&#8217; \u5177\u6709\u4e0e\u77e9\u9635 A \u76f8\u540c\u7684\u975e 0 2\u00d72 \u884c\u5217\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-a5d1acad8bc31240f80d8cfbf3605997_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} 3 &amp; 2 \\\\[1.1ex] -2 &amp; 3 \\end{vmatrix} =9-(-4)=13\\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"222\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c<strong>\u77e9\u9635 A&#8217; \u7684\u79e9\u4e5f\u662f 2<\/strong> \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-80398cfd2fff647f81c0d4160f3b2f7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  rg(A')=2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"81\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u7531\u4e8e\u77e9\u9635 A \u7684\u79e9\u7b49\u4e8e\u77e9\u9635 A&#8217; \u7684\u79e9\uff0c\u4f46\u8fd9\u4e24\u4e2a\u503c\u5747\u5c0f\u4e8e\u7cfb\u7edf (3) \u7684\u672a\u77e5\u6570\u4e2a\u6570\uff0c\u56e0\u6b64\u6839\u636e<strong>Rouch\u00e9-Frobenius \u5b9a\u7406<\/strong>\u53ef\u77e5\uff0c\u8fd9\u662f\u4e00\u4e2a<strong>\u4e0d\u5b9a\u76f8\u5bb9\u7cfb\u7edf<\/strong>\uff08\u5de5\u4e1a\u63a7\u5236\u7cfb\u7edf\uff09\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-96868a2569ea0ab5ca99d8dc606d3dc9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{array}{c} \\begin{array}{c} \\color{black}rg(A) = 2 \\\\[1.3ex] \\color{black}rg(A')=2 \\\\[1.3ex] \\color{black}\\text{N\\'umero de inc\\'ognitas} = 3    \\end{array}} \\\\ \\\\  \\color{blue} \\boxed{ \\color{black}\\phantom{^9_9} rg(A) = rg(A') = 2 \\ < \\ n =3  \\color{blue} \\ \\bm{\\longrightarrow} \\ \\color{black} \\bm{SCI}\\phantom{^9_9}} \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"138\" width=\"475\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-background\" style=\"background-color:#dff6ff\">\u5f53\u6211\u4eec\u60f3\u8981\u6c42\u89e3\u76f8\u5bb9\u4e0d\u5b9a\u7cfb\u7edf\uff08SCI\uff09\u65f6\uff0c\u6211\u4eec\u9700\u8981<strong>\u5bf9\u7cfb\u7edf\u8fdb\u884c\u53d8\u6362<\/strong>\uff1a\u9996\u5148\u6d88\u53bb\u4e00\u4e2a\u65b9\u7a0b\uff0c\u7136\u540e\u5c06\u4e00\u4e2a\u53d8\u91cf\u8f6c\u6362\u4e3a \u03bb\uff08\u901a\u5e38\u662f\u53d8\u91cf z\uff09\uff0c\u6700\u540e\u5c06 \u03bb \u9879\u4e0e\u72ec\u7acb\u6761\u6b3e\u3002<\/p>\n<p>\u4e00\u65e6\u6211\u4eec\u6539\u9020\u4e86\u7cfb\u7edf\uff0c\u6211\u4eec\u5e94\u7528\u514b\u62c9\u9ed8\u89c4\u5219\uff0c\u6211\u4eec\u5c06\u83b7\u5f97\u7cfb\u7edf\u4f5c\u4e3a \u03bb \u51fd\u6570\u7684\u89e3\u3002<\/p>\n<p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c<strong>\u6211\u4eec\u5c06\u4ece\u7cfb\u7edf\u4e2d\u6d88\u9664\u6700\u540e\u4e00\u4e2a\u65b9\u7a0b<\/strong>\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-f0511fecc9c2af695b6b8eccae6b0661_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases} 3x+2y+4z=1 \\\\[1.5ex] -2x+3y-z=0 \\\\[1.5ex]\\cancel{x+5y+3z = 1} \\end{cases} \\longrightarrow \\quad \\begin{cases} 3x+2y+4z=1 \\\\[1.5ex] -2x+3y-z=0\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"377\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p><strong>\u73b0\u5728\u8ba9\u6211\u4eec\u5c06\u53d8\u91cf z \u8f6c\u6362\u4e3a \u03bb\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-2d6142d2be611954fd849a032a97245a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases} 3x+2y+4z=1 \\\\[1.5ex] -2x+3y-z=0  \\end{cases} \\xrightarrow{z \\ = \\ \\lambda}\\quad \\begin{cases} 3x+2y+4\\lambda=1 \\\\[1.5ex] -2x+3y-\\lambda=0\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"398\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u5c06<strong>\u5e26\u6709 \u03bb \u7684\u9879\u4e0e\u72ec\u7acb\u9879\u653e\u5728\u4e00\u8d77\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-00214205f2334f1c9bc10810c1c1df83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases} 3x+2y=1-4\\lambda \\\\[1.5ex] -2x+3y=\\lambda \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"145\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"adsb30\" style=\" margin:px; text-align:\"><\/div>\n<p>\u56e0\u6b64\uff0c\u7cfb\u7edf\u7684\u77e9\u9635A\u548c\u77e9\u9635A&#8217;\u4ecd\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-9c4b47303973b823a1c5628f5448ca79_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A= \\left( \\begin{array}{ccc} 3 &amp; 2  \\\\[1.1ex] -2 &amp; 3 \\end{array} \\right) \\qquad A'= \\left( \\begin{array}{cc|c} 3 &amp; 2 &amp; 1 -4\\lambda \\\\[1.1ex] -2 &amp; 3 &amp; \\lambda \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"363\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6700\u540e\uff0c\u4e00\u65e6\u6211\u4eec\u6539\u53d8\u4e86\u7cfb\u7edf\uff0c<strong>\u6211\u4eec\u5c31\u5e94\u7528\u514b\u83b1\u9ed8\u89c4\u5219<\/strong>\u3002\u56e0\u6b64\u6211\u4eec\u6c42\u89e3 A \u7684\u884c\u5217\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-d1b79f52dc82f5cfc311867273e78c06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix}A \\end{vmatrix}= \\begin{vmatrix} 3 &amp; 2  \\\\[1.1ex] -2 &amp; 3\\end{vmatrix} = 13\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"148\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u8ba1\u7b97\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-757d0eed520b26d08cc3b8b397d0f980_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u6839\u636e\u514b\u83b1\u9ed8\u89c4\u5219\uff0c\u6211\u4eec\u5c06 A \u884c\u5217\u5f0f\u7684\u7b2c\u4e00\u5217\u66f4\u6539\u4e3a\u72ec\u7acb\u9879\u5217\uff0c\u7136\u540e\u5c06\u5176\u9664\u4ee5 A \u7684\u884c\u5217\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-0ff917eaea976c65bd18e0476078d3cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{x} = \\cfrac{\\begin{vmatrix} 1 -4\\lambda &amp; 2  \\\\[1.1ex] \\lambda &amp; 3 \\end{vmatrix}}{\\begin{vmatrix} A \\end{vmatrix}} = \\cfrac{3(1-4\\lambda) -2\\lambda}{13} = \\cfrac{\\bm{3-14\\lambda} }{\\bm{13}}\" title=\"Rendered by QuickLaTeX.com\" height=\"81\" width=\"349\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u8ba1\u7b97\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-5fb4fb8b1addff607711094fd1ed326e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u6839\u636e\u514b\u83b1\u9ed8\u89c4\u5219\uff0c\u6211\u4eec\u5c06 A \u884c\u5217\u5f0f\u7684\u7b2c\u4e8c\u5217\u66f4\u6539\u4e3a\u72ec\u7acb\u9879\u5217\uff0c\u5e76\u5c06\u5176\u9664\u4ee5 A \u7684\u884c\u5217\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-155ca520739bbf7e040a6cdc632f7c27_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{y} = \\cfrac{\\begin{vmatrix} 3 &amp; 1 -4\\lambda  \\\\[1.1ex]-2&amp;  \\lambda  \\end{vmatrix}}{\\begin{vmatrix} A \\end{vmatrix}} = \\cfrac{3\\lambda -\\bigl(-2(1-4\\lambda)\\bigr)}{13}= \\cfrac{3\\lambda -\\bigl(-2+8\\lambda\\bigr)}{13} = \\cfrac{\\bm{2-5\\lambda} }{\\bm{13}}\" title=\"Rendered by QuickLaTeX.com\" height=\"81\" width=\"529\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u867d\u7136\u65b9\u7a0b\u7ec4\u7684\u89e3\u662f \u03bb \u7684\u51fd\u6570\uff0c\u4f46\u7531\u4e8e\u5b83\u662f SCI\uff0c\u56e0\u6b64\u5b83\u6709\u65e0\u7a77\u591a\u4e2a\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-c9866e045041eb2d8fe103db2309f229_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{x =} \\cfrac{\\bm{3-14\\lambda} }{\\bm{13}} \\qquad \\bm{y=}\\cfrac{\\bm{2-5\\lambda} }{\\bm{13}} \\qquad \\bm{z = \\lambda}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"283\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\">\u514b\u83b1\u9ed8\u6cd5\u5219\u89e3\u51b3\u4e86\u95ee\u9898<\/h2>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-118\"><\/div>\n<\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u5e94\u7528\u514b\u83b1\u9ed8\u6cd5\u5219\u6c42\u89e3\u4ee5\u4e0b\u5177\u6709 2 \u4e2a\u672a\u77e5\u6570\u7684\u4e24\u4e2a\u65b9\u7a0b\u7ec4\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-pas-a-pas-de-la-regle-de-cramer-22.webp\" alt=\"\u4f7f\u7528 Cramer \u7684 2x2 \u89c4\u5219\u9010\u6b65\u89e3\u51b3\u7ec3\u4e60\" class=\"wp-image-3999\" width=\"137\" height=\"83\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\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\">\u9996\u5148\u8981\u505a\u7684\u662f\u7cfb\u7edf\u7684\u77e9\u9635A\u548c\u6269\u5c55\u77e9\u9635A&#8217;\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-2a001db9cf56846150730fee7126dacd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A= \\left( \\begin{array}{cc} 2 &amp; 5 \\\\[1.1ex] 1 &amp; 4 \\end{array} \\right) \\qquad A'= \\left( \\begin{array}{cc|c} 2 &amp; 5 &amp; 8 \\\\[1.1ex] 1 &amp; 4 &amp; 7 \\end{array}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"294\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u73b0\u5728\u5fc5\u987b\u627e\u5230\u77e9\u9635 A \u7684\u79e9\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u68c0\u67e5\u6574\u4e2a\u77e9\u9635\u7684\u884c\u5217\u5f0f\u662f\u5426\u4e0d\u4e3a 0\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-0c75c1c344c286016bea83237f1f418e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix}A \\end{vmatrix}= \\begin{vmatrix} 2 &amp; 5 \\\\[1.1ex] 1 &amp; 4 \\end{vmatrix} = 8-5=3 \\bm{\\neq 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"216\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7531\u4e8e\u77e9\u9635\u5177\u6709\u4e0d\u540c\u4e8e 0 \u7684 2\u00d72 \u884c\u5217\u5f0f\uff0c<strong>\u56e0\u6b64\u77e9\u9635 A \u7684\u79e9\u4e3a 2\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-eded270b78ab3d95ce827e3ea428efb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  rg(A)=2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"76\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e00\u65e6\u6211\u4eec\u77e5\u9053\u4e86 A \u7684\u7b49\u7ea7\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u8ba1\u7b97 A&#8217; \u7684\u7b49\u7ea7\u3002\u8fd9\u81f3\u5c11\u662f 2 \u9636\u7684\uff0c\u56e0\u4e3a\u6211\u4eec\u521a\u521a\u770b\u5230\u5b83\u5185\u90e8\u6709\u4e00\u4e2a\u4e0d\u540c\u4e8e 0 \u7684 2 \u9636\u884c\u5217\u5f0f\u3002\u6b64\u5916\uff0c\u5b83\u4e0d\u53ef\u80fd\u662f 3 \u9636\u7684\uff0c\u56e0\u4e3a\u6211\u4eec\u4e0d\u80fd\u4e0d\u505a\u4e00\u4e2a 3\u00d73 \u884c\u5217\u5f0f\u3002\u56e0\u6b64\uff0c<strong>\u77e9\u9635 A&#8217; \u7684\u79e9\u4e5f\u662f 2\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-80398cfd2fff647f81c0d4160f3b2f7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  rg(A')=2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"81\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u901a\u8fc7\u5e94\u7528<strong>Rouch\u00e9-Frobenius\u5b9a\u7406\uff0c<\/strong>\u6211\u4eec\u77e5\u9053\u8fd9\u662f\u4e00\u4e2a<strong>\u517c\u5bb9\u7684\u786e\u5b9a\u7cfb\u7edf<\/strong>\uff08SCD\uff09\uff0c\u56e0\u4e3aA\u7684\u8303\u56f4\u7b49\u4e8eA&#8217;\u7684\u8303\u56f4\u548c\u672a\u77e5\u6570\u7684\u6570\u91cf\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-bbd67b16bb6d52a0696e70a77833cd3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{array}{c} \\begin{array}{c} \\color{black}rg(A) = 2 \\\\[1.3ex] \\color{black}rg(A')=2 \\\\[1.3ex] \\color{black}\\text{N\\'umero de inc\\'ognitas} = 2 \\end{array}} \\\\ \\\\ \\color{blue} \\boxed{ \\color{black}\\phantom{^9_9} rg(A) = rg(A') = n = 2 \\color{blue} \\ \\bm{\\longrightarrow} \\ \\color{black} \\bm{SCD}\\phantom{^9_9}} \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"138\" width=\"436\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e00\u65e6\u6211\u4eec\u77e5\u9053\u7cfb\u7edf\u662f\u4e00\u4e2a SCD\uff0c\u6211\u4eec\u5c31\u5e94\u7528<strong>\u514b\u83b1\u9ed8\u89c4\u5219<\/strong>\u6765\u89e3\u51b3\u5b83\u3002<\/p>\n<p class=\"has-text-align-left\">\u8ba1\u7b97\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-757d0eed520b26d08cc3b8b397d0f980_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u6839\u636e\u514b\u83b1\u9ed8\u89c4\u5219\uff0c\u6211\u4eec\u5c06 A \u884c\u5217\u5f0f\u7684\u7b2c\u4e00\u5217\u66f4\u6539\u4e3a\u72ec\u7acb\u9879\u5217\uff0c\u7136\u540e\u5c06\u5176\u9664\u4ee5 A \u7684\u884c\u5217\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-b0adeda8f2ce557661466996038b1148_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{x} = \\cfrac{\\begin{vmatrix} 8 &amp; 5 \\\\[1.1ex] 7 &amp; 4\\end{vmatrix}}{\\begin{vmatrix} A \\end{vmatrix}} = \\cfrac{-3}{3} = \\bm{-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"81\" width=\"186\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8ba1\u7b97\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-5fb4fb8b1addff607711094fd1ed326e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u6839\u636e\u514b\u83b1\u9ed8\u89c4\u5219\uff0c\u6211\u4eec\u5c06 A \u884c\u5217\u5f0f\u7684\u7b2c\u4e8c\u5217\u66f4\u6539\u4e3a\u72ec\u7acb\u9879\u5217\uff0c\u5e76\u5c06\u5176\u9664\u4ee5 A \u7684\u884c\u5217\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-59790a66cc31fac07be1d5a7bb556d9e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{y} = \\cfrac{\\begin{vmatrix}2 &amp; 8 \\\\[1.1ex] 1 &amp; 7\\end{vmatrix}}{\\begin{vmatrix} A \\end{vmatrix}} = \\cfrac{6}{3} = \\bm{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"81\" width=\"150\" 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-26fa7c9ed2d05ca07ff62a968ba7ab11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{x = -1 \\qquad y=2}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"133\" 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\u514b\u83b1\u9ed8\u6cd5\u5219\u6c42\u4ee5\u4e0b\u5177\u6709 3 \u4e2a\u672a\u77e5\u6570\u7684\u4e09\u4e2a\u65b9\u7a0b\u7ec4\u7684\u89e3\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-du-systeme-de-regles-de-cramer-des-equations-3-3.webp\" alt=\"\u89e3\u51b3\u4e86 3x3 \u65b9\u7a0b\u7ec4\u514b\u83b1\u9ed8\u89c4\u5219\u7684\u7ec3\u4e60\" class=\"wp-image-4002\" width=\"181\" height=\"124\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\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\u5236\u4f5c\u7cfb\u7edf\u7684\u77e9\u9635A\u548c\u6269\u5c55\u77e9\u9635A&#8217;\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-eea75fbf6d86ebc3d0b9e236cd2160f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A= \\left( \\begin{array}{ccc} 1 &amp; 3 &amp; 2\\\\[1.1ex] -1 &amp; 5 &amp; -1\\\\[1.1ex] 3 &amp; -1 &amp; 4 \\end{array} \\right) \\qquad A'= \\left( \\begin{array}{ccc|c} 1 &amp; 3 &amp; 2 &amp; 2 \\\\[1.1ex] -1 &amp; 5 &amp; -1 &amp; 4 \\\\[1.1ex] 3 &amp; -1 &amp; 4 &amp; 0 \\end{array}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"432\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\uff0c\u6211\u4eec\u901a\u8fc7\u4f7f\u7528 Sarrus \u89c4\u5219\u8ba1\u7b97 3\u00d73 \u77e9\u9635\u7684\u884c\u5217\u5f0f\u6765\u627e\u5230\u77e9\u9635 A \u7684\u79e9\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-73f751f3b5c527c16b5de1b10bf07a4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix}A \\end{vmatrix}= \\begin{vmatrix} 1 &amp; 3 &amp; 2 \\\\[1.1ex] -1 &amp; 5 &amp; -1\\\\[1.1ex] 3 &amp; -1 &amp; 4 \\end{vmatrix} = 20-9+2-30-1+12=-6 \\bm{\\neq 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"445\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5177\u6709\u4e0d\u540c\u4e8e 0 \u7684 3 \u9636\u884c\u5217\u5f0f\u7684\u77e9\u9635\uff0c<strong>\u77e9\u9635 A \u7684\u79e9\u4e3a 3\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-842ae3b68df41813d9e409968f3ae946_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  rg(A)=3\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"77\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u77e9\u9635 A&#8217; \u7684\u79e9\u4e5f\u662f 3\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-150bbc9c8e363db471c2d5bc4f33e1fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  rg(A')=3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"82\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u5229\u7528<strong>Rouch\u00e9-Frobenius \u5b9a\u7406\uff0c<\/strong>\u6211\u4eec\u77e5\u9053\u8fd9\u662f\u4e00\u4e2a<strong>\u517c\u5bb9\u7684\u786e\u5b9a\u7cfb\u7edf<\/strong>\uff08SCD\uff09\uff0c\u56e0\u4e3a A \u7684\u8303\u56f4\u7b49\u4e8e A&#8217; \u7684\u8303\u56f4\u548c\u672a\u77e5\u6570\u7684\u6570\u91cf\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-31b495a48a75d7af1f23e38818bf4eca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{array}{c} \\begin{array}{c} \\color{black}rg(A) = 3 \\\\[1.3ex] \\color{black}rg(A')=3 \\\\[1.3ex] \\color{black}\\text{N\\'umero de inc\\'ognitas} = 3 \\end{array}} \\\\ \\\\ \\color{blue} \\boxed{ \\color{black}\\phantom{^9_9} rg(A) = rg(A') = n = 3 \\color{blue} \\ \\bm{\\longrightarrow} \\ \\color{black} \\bm{SCD}\\phantom{^9_9}} \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"138\" width=\"436\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e00\u65e6\u6211\u4eec\u77e5\u9053\u8be5\u7cfb\u7edf\u662f\u4e00\u4e2aSCD\uff0c\u6211\u4eec\u5c31\u9700\u8981\u5e94\u7528<strong>\u514b\u83b1\u9ed8\u89c4\u5219<\/strong>\u6765\u6c42\u89e3\u8be5\u7cfb\u7edf\u3002<\/p>\n<p class=\"has-text-align-left\">\u8ba1\u7b97\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-757d0eed520b26d08cc3b8b397d0f980_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u6839\u636e\u514b\u83b1\u9ed8\u89c4\u5219\uff0c\u6211\u4eec\u5c06 A \u884c\u5217\u5f0f\u7684\u7b2c\u4e00\u5217\u66f4\u6539\u4e3a\u72ec\u7acb\u9879\u5217\uff0c\u7136\u540e\u5c06\u5176\u9664\u4ee5 A \u7684\u884c\u5217\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-fc574297f609b68e4fb48466ec6c8077_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{x} = \\cfrac{\\begin{vmatrix} 2 &amp; 3 &amp; 2 \\\\[1.1ex] 4 &amp; 5 &amp; -1\\\\[1.1ex]0 &amp; -1 &amp; 4\\end{vmatrix}}{\\begin{vmatrix} A \\end{vmatrix}} = \\cfrac{-18}{-6} = \\bm{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"113\" width=\"235\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8ba1\u7b97\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-5fb4fb8b1addff607711094fd1ed326e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u6839\u636e\u514b\u83b1\u9ed8\u89c4\u5219\uff0c\u6211\u4eec\u5c06 A \u884c\u5217\u5f0f\u7684\u7b2c\u4e8c\u5217\u66f4\u6539\u4e3a\u72ec\u7acb\u9879\u5217\uff0c\u5e76\u5c06\u5176\u9664\u4ee5 A \u7684\u884c\u5217\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-2544601137d62e217ff1866f278203d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{y} = \\cfrac{\\begin{vmatrix}1 &amp; 2 &amp; 2 \\\\[1.1ex] -1 &amp; 4 &amp; -1\\\\[1.1ex] 3 &amp; 0 &amp; 4\\end{vmatrix}}{\\begin{vmatrix} A \\end{vmatrix}} = \\cfrac{-6}{-6} = \\bm{1}\" title=\"Rendered by QuickLaTeX.com\" height=\"113\" width=\"224\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8ba1\u7b97<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-23aa090e6102a41de5ad5515112e4d03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  z\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u6839\u636e\u514b\u83b1\u9ed8\u89c4\u5219\uff0c\u6211\u4eec\u5c06 A \u884c\u5217\u5f0f\u7684\u7b2c\u4e09\u5217\u66f4\u6539\u4e3a\u72ec\u7acb\u9879\u5217\uff0c\u5e76\u5c06\u5176\u9664\u4ee5 A \u7684\u884c\u5217\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-42d7d4adcfc48954185ca14b56b8e128_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{z} = \\cfrac{\\begin{vmatrix} 1 &amp; 3 &amp; 2 \\\\[1.1ex] -1 &amp; 5 &amp; 4 \\\\[1.1ex] 3 &amp; -1 &amp; 0\\end{vmatrix}}{\\begin{vmatrix} A \\end{vmatrix}} = \\cfrac{12}{-6} = \\bm{-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"113\" width=\"230\" 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-685195d3a299f30f6421bb387f7f00e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{x =3 \\qquad y=1 \\qquad z=-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"210\" 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\u4e603<\/h3>\n<p>\u4f7f\u7528\u514b\u83b1\u9ed8\u6cd5\u5219\u8ba1\u7b97\u4ee5\u4e0b\u5177\u6709 3 \u4e2a\u672a\u77e5\u6570\u7684\u4e09\u4e2a\u65b9\u7a0b\u7ec4\u7684\u89e3\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\/exemple-de-regle-de-cramer.webp\" alt=\"\u514b\u83b1\u9ed8\u89c4\u5219\u7684\u793a\u4f8b\" class=\"wp-image-4003\" width=\"183\" height=\"123\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\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\u5236\u4f5c\u7cfb\u7edf\u7684\u77e9\u9635A\u548c\u6269\u5c55\u77e9\u9635A&#8217;\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-afd359275e5ebaaf3229504c47a5815f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A= \\left( \\begin{array}{ccc} 1 &amp; 2 &amp; 5\\\\[1.1ex] 2 &amp; 3 &amp; -1 \\\\[1.1ex] 3 &amp; 4 &amp; -7 \\end{array} \\right) \\qquad A'= \\left( \\begin{array}{ccc|c} 1 &amp; 2 &amp; 5 &amp; 1 \\\\[1.1ex] 2 &amp; 3 &amp; -1 &amp; 5 \\\\[1.1ex] 3 &amp; 4 &amp; -7 &amp; 9 \\end{array}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"377\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u8ba1\u7b97\u77e9\u9635 A \u7684\u8303\u56f4\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-47ddf17a2b3eed5a680d685900a79b31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix}A \\end{vmatrix}= \\begin{vmatrix} 1 &amp; 2 &amp; 5\\\\[1.1ex] 2 &amp; 3 &amp; -1 \\\\[1.1ex] 3 &amp; 4 &amp; -7 \\end{vmatrix} =-21-6+40-45+4+28=0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"398\" 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-fdd4380c7c76418bd3ec12c94359f886_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} 1 &amp; 2 \\\\[1.1ex] 2 &amp; 3  \\end{vmatrix} = 3-4 = -1 \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"186\" 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-eded270b78ab3d95ce827e3ea428efb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  rg(A)=2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"76\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e00\u65e6\u6211\u4eec\u77e5\u9053\u4e86\u77e9\u9635 A \u7684\u8303\u56f4\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u8ba1\u7b97\u77e9\u9635 A&#8217; \u7684\u8303\u56f4\u3002\u524d 3 \u5217\u7684\u884c\u5217\u5f0f\u7ed9\u51fa 0\uff0c\u56e0\u6b64\u6211\u4eec\u5c1d\u8bd5\u77e9\u9635 A&#8217; \u4e2d\u5176\u4ed6\u53ef\u80fd\u7684 3\u00d73 \u884c\u5217\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-1addc62130e0462075b3bade26a7e35e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} 2 &amp; 5 &amp; 1 \\\\[1.1ex]  3 &amp; -1 &amp; 5 \\\\[1.1ex] 4 &amp; -7 &amp; 9 \\end{vmatrix} = 0 \\qquad \\begin{vmatrix} 1 &amp; 5 &amp; 1 \\\\[1.1ex] 2 &amp; -1 &amp; 5 \\\\[1.1ex] 3 &amp; -7 &amp; 9\\end{vmatrix} = 0 \\qquad \\begin{vmatrix} 1 &amp; 2 &amp; 1 \\\\[1.1ex] 2 &amp; 3 &amp; 5 \\\\[1.1ex] 3 &amp; 4 &amp; 9 \\end{vmatrix} = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"412\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6240\u6709 3 \u9636\u884c\u5217\u5f0f\u90fd\u7ed9\u51fa 0\u3002\u7136\u800c\uff0c\u77e9\u9635 A&#8217; \u5177\u6709\u4e0e\u77e9\u9635 A \u76f8\u540c\u7684 2\u00d72 \u975e 0 \u884c\u5217\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-7de377466bd5afd03f58f9b532324e75_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} 1 &amp; 2 \\\\[1.1ex] 2 &amp; 3 \\end{vmatrix} = 3-4 = -1 \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"186\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u77e9\u9635 A&#8217; \u7684\u79e9\u4e5f\u662f 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-80398cfd2fff647f81c0d4160f3b2f7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  rg(A')=2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"81\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7531\u4e8e\u77e9\u9635 A \u7684\u79e9\u7b49\u4e8e\u77e9\u9635 A&#8217; \u7684\u79e9\uff0c\u4f46\u8fd9\u4e24\u8005\u90fd\u5c0f\u4e8e\u7cfb\u7edf (3) \u7684\u672a\u77e5\u6570\u4e2a\u6570\uff0c\u56e0\u6b64\u6839\u636e<strong>Rouch\u00e9-Frobenius \u5b9a\u7406<\/strong>\u53ef\u77e5\u5b83\u662f\u4e00\u4e2a<strong>\u4e0d\u5b9a\u76f8\u5bb9\u7cfb\u7edf<\/strong>(ICS)\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-96868a2569ea0ab5ca99d8dc606d3dc9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{array}{c} \\begin{array}{c} \\color{black}rg(A) = 2 \\\\[1.3ex] \\color{black}rg(A')=2 \\\\[1.3ex] \\color{black}\\text{N\\'umero de inc\\'ognitas} = 3    \\end{array}} \\\\ \\\\  \\color{blue} \\boxed{ \\color{black}\\phantom{^9_9} rg(A) = rg(A') = 2 \\ < \\ n =3  \\color{blue} \\ \\bm{\\longrightarrow} \\ \\color{black} \\bm{SCI}\\phantom{^9_9}} \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"138\" width=\"475\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4f5c\u4e3a ICS \u7cfb\u7edf\uff0c\u6211\u4eec\u5fc5\u987b\u6d88\u9664\u4e00\u4e2a\u65b9\u7a0b\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c<strong>\u6211\u4eec\u5c06\u4ece\u7cfb\u7edf\u4e2d\u6d88\u9664\u6700\u540e\u4e00\u4e2a\u65b9\u7a0b<\/strong>\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-3a1d067e155540f4345cf56e5c1567d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases} x+2y+5z=1 \\\\[1.5ex] 2x+3y-z=5 \\\\[1.5ex]\\cancel{3x+4y-7z = 9} \\end{cases} \\longrightarrow \\quad \\begin{cases} x+2y+5z=1 \\\\[1.5ex] 2x+3y-z=5\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"357\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"><strong>\u73b0\u5728\u8ba9\u6211\u4eec\u5c06\u53d8\u91cf z \u8f6c\u6362\u4e3a \u03bb\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-b5fa91777a722d3783b2f887aab44152_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases} x+2y+5z=1 \\\\[1.5ex] 2x+3y-z=5  \\end{cases} \\xrightarrow{z \\ = \\ \\lambda}\\quad \\begin{cases} x+2y+5\\lambda=1 \\\\[1.5ex] 2x+3y-\\lambda=5\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"369\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u5c06\u5e26\u6709 \u03bb \u7684\u9879\u4e0e\u72ec\u7acb\u9879\u653e\u5728\u4e00\u8d77\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-76ff21181be050b01c247981298986a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases} x+2y=1-5\\lambda\\\\[1.5ex] 2x+3y=5+\\lambda \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"136\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4f7f\u5f97\u7cfb\u7edf\u7684\u77e9\u9635A\u548c\u77e9\u9635A&#8217;\u4fdd\u6301\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-230e5b28dd467127e63f4f9756cf90da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A= \\left( \\begin{array}{ccc} 1 &amp; 2  \\\\[1.1ex] 2 &amp; 3 \\end{array} \\right) \\qquad A'= \\left( \\begin{array}{cc|c} 1 &amp; 2 &amp; 1 -5\\lambda \\\\[1.1ex] 2 &amp; 3 &amp;5+\\lambda \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"335\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\uff0c\u4e00\u65e6\u6211\u4eec\u6539\u53d8\u4e86\u7cfb\u7edf\uff0c<strong>\u6211\u4eec\u5c31\u5e94\u7528\u514b\u83b1\u9ed8\u89c4\u5219<\/strong>\u3002\u56e0\u6b64\u6211\u4eec\u6c42\u89e3 A \u7684\u884c\u5217\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-f127efbd217e2bca8852ec792610732f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix}A \\end{vmatrix}= \\begin{vmatrix} 1 &amp; 2 \\\\[1.1ex] 2 &amp; 3\\end{vmatrix} =-1\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"138\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8ba1\u7b97\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-757d0eed520b26d08cc3b8b397d0f980_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u6839\u636e\u514b\u83b1\u9ed8\u89c4\u5219\uff0c\u6211\u4eec\u5c06 A \u884c\u5217\u5f0f\u7684\u7b2c\u4e00\u5217\u66f4\u6539\u4e3a\u72ec\u7acb\u9879\u5217\uff0c\u7136\u540e\u5c06\u5176\u9664\u4ee5 A \u7684\u884c\u5217\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-42652a14362b42e606841b6bb3e77cc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{x} = \\cfrac{\\begin{vmatrix} 1-5\\lambda &amp; 2 \\\\[1.1ex] 5+\\lambda &amp; 3 \\end{vmatrix}}{\\begin{vmatrix} A \\end{vmatrix}} = \\cfrac{3-15\\lambda -(10+2\\lambda)}{-1} = \\cfrac{-7-17\\lambda}{-1} = \\bm{7+17\\lambda}\" title=\"Rendered by QuickLaTeX.com\" height=\"81\" width=\"491\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8ba1\u7b97\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-5fb4fb8b1addff607711094fd1ed326e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u6839\u636e\u514b\u83b1\u9ed8\u89c4\u5219\uff0c\u6211\u4eec\u5c06 A \u884c\u5217\u5f0f\u7684\u7b2c\u4e8c\u5217\u66f4\u6539\u4e3a\u72ec\u7acb\u9879\u5217\uff0c\u5e76\u5c06\u5176\u9664\u4ee5 A \u7684\u884c\u5217\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-b95c5870f1762a2d82c9ebcccbca7408_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{y} = \\cfrac{\\begin{vmatrix} 1 &amp; 1-5\\lambda \\\\[1.1ex] 2 &amp; 5+\\lambda \\end{vmatrix}}{\\begin{vmatrix} A \\end{vmatrix}} = \\cfrac{5+\\lambda -(2-10\\lambda)}{-1}= \\cfrac{3+11\\lambda}{-1} = \\bm{-3-11\\lambda}\" title=\"Rendered by QuickLaTeX.com\" height=\"81\" width=\"465\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u867d\u7136\u65b9\u7a0b\u7ec4\u7684\u89e3\u662f \u03bb \u7684\u51fd\u6570\uff0c\u4f46\u7531\u4e8e\u5b83\u662f SCI\uff0c\u56e0\u6b64\u5b83\u6709\u65e0\u7a77\u591a\u4e2a\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-5483357f081aca551b07fe7c8f9ebf5d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{x =7+17\\lambda} \\qquad \\bm{y=-3-11\\lambda} \\qquad \\bm{z = \\lambda}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"311\" 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\u4e604<\/h3>\n<p>\u5e94\u7528\u514b\u83b1\u9ed8\u89c4\u5219\u6c42\u89e3\u4ee5\u4e0b\u5177\u6709 3 \u4e2a\u672a\u77e5\u6570\u7684\u4e09\u65b9\u7a0b\u7ec4\u95ee\u9898\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-61e1c3458f33b863db10750b9e51d09e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases} -2x+5y+z=8 \\\\[1.5ex] 6x+2y+4z=4 \\\\[1.5ex] 3x-2y+z = -2 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"149\" 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\">\u9996\u5148\u6784\u9020\u7cfb\u7edf\u7684\u77e9\u9635A\u548c\u6269\u5c55\u77e9\u9635A&#8217;\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-743a40010cb4a610e8a3fc6ae5d313b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A= \\left( \\begin{array}{ccc}-2 &amp; 5 &amp; 1 \\\\[1.1ex] 6 &amp; 2 &amp; 4 \\\\[1.1ex] 3 &amp; -2 &amp; 1\\end{array} \\right) \\qquad A'= \\left( \\begin{array}{ccc|c} -2 &amp; 5 &amp; 1 &amp; 8 \\\\[1.1ex] 6 &amp; 2 &amp; 4 &amp; 4 \\\\[1.1ex] 3 &amp; -2 &amp; 1 &amp; -2 \\end{array}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"419\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u8ba9\u6211\u4eec\u901a\u8fc7\u4f7f\u7528 Sarrus \u89c4\u5219\u8ba1\u7b97 3&#215;3 \u77e9\u9635\u7684\u884c\u5217\u5f0f\u6765\u8ba1\u7b97\u77e9\u9635 A \u7684\u79e9\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-713c634fbc3e1b1cb228e3891c9bff1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix}A \\end{vmatrix}= \\begin{vmatrix} -2 &amp; 5 &amp; 1 \\\\[1.1ex] 6 &amp; 2 &amp; 4 \\\\[1.1ex] 3 &amp; -2 &amp; 1 \\end{vmatrix} = -4+60-12-6-16-30=-8 \\bm{\\neq 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"453\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5177\u6709\u4e0d\u540c\u4e8e 0 \u7684 3 \u9636\u884c\u5217\u5f0f\u7684\u77e9\u9635\uff0c<strong>\u77e9\u9635 A \u7684\u79e9\u4e3a 3\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-842ae3b68df41813d9e409968f3ae946_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  rg(A)=3\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"77\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u77e9\u9635 A&#8217; \u7684\u79e9\u4e5f\u662f 3\uff0c\u56e0\u4e3a\u5b83\u5fc5\u987b\u81f3\u5c11\u4e0e\u77e9\u9635 A \u5177\u6709\u76f8\u540c\u7684\u79e9\uff0c\u5e76\u4e14\u5b83\u4e0d\u80fd\u662f\u79e9 4\uff0c\u56e0\u4e3a\u5b83\u662f\u7ef4\u5ea6\u4e3a 3\u00d74 \u7684\u77e9\u9635\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-150bbc9c8e363db471c2d5bc4f33e1fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  rg(A')=3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"82\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u5229\u7528<strong>Rouch\u00e9-Frobenius \u5b9a\u7406\uff0c<\/strong>\u6211\u4eec\u63a8\u65ad\u5b83\u662f\u4e00\u4e2a<strong>\u786e\u5b9a\u517c\u5bb9\u7cfb\u7edf<\/strong>\uff08SCD\uff09\uff0c\u56e0\u4e3a A \u7684\u8303\u56f4\u7b49\u4e8e A&#8217; \u7684\u8303\u56f4\u548c\u672a\u77e5\u6570\u7684\u6570\u91cf\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-31b495a48a75d7af1f23e38818bf4eca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{array}{c} \\begin{array}{c} \\color{black}rg(A) = 3 \\\\[1.3ex] \\color{black}rg(A')=3 \\\\[1.3ex] \\color{black}\\text{N\\'umero de inc\\'ognitas} = 3 \\end{array}} \\\\ \\\\ \\color{blue} \\boxed{ \\color{black}\\phantom{^9_9} rg(A) = rg(A') = n = 3 \\color{blue} \\ \\bm{\\longrightarrow} \\ \\color{black} \\bm{SCD}\\phantom{^9_9}} \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"138\" width=\"436\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e00\u65e6\u6211\u4eec\u77e5\u9053\u8be5\u7cfb\u7edf\u662f\u4e00\u4e2aSCD\uff0c\u6211\u4eec\u5c31\u9700\u8981\u5e94\u7528<strong>\u514b\u83b1\u9ed8\u89c4\u5219<\/strong>\u6765\u6c42\u89e3\u8be5\u7cfb\u7edf\u3002<\/p>\n<p class=\"has-text-align-left\">\u8ba1\u7b97\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-757d0eed520b26d08cc3b8b397d0f980_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u6839\u636e\u514b\u83b1\u9ed8\u89c4\u5219\uff0c\u6211\u4eec\u5c06 A \u884c\u5217\u5f0f\u7684\u7b2c\u4e00\u5217\u66f4\u6539\u4e3a\u72ec\u7acb\u9879\u5217\uff0c\u7136\u540e\u5c06\u5176\u9664\u4ee5 A \u7684\u884c\u5217\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-8a290479c69ff806f19dcf29f96e1228_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{x} = \\cfrac{\\begin{vmatrix} 8 &amp; 5 &amp; 1 \\\\[1.1ex] 4 &amp; 2 &amp; 4 \\\\[1.1ex] -2 &amp; -2 &amp; 1\\end{vmatrix}}{\\begin{vmatrix} A \\end{vmatrix}} = \\cfrac{16}{-8} = \\bm{-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"113\" width=\"231\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8ba1\u7b97\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-5fb4fb8b1addff607711094fd1ed326e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u6839\u636e\u514b\u83b1\u9ed8\u89c4\u5219\uff0c\u6211\u4eec\u5c06 A \u884c\u5217\u5f0f\u7684\u7b2c\u4e8c\u5217\u66f4\u6539\u4e3a\u72ec\u7acb\u9879\u5217\uff0c\u5e76\u5c06\u5176\u9664\u4ee5 A \u7684\u884c\u5217\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-8bba0765fbcbcebf0585520af25b4a30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{y} = \\cfrac{\\begin{vmatrix}-2 &amp; 8 &amp; 1 \\\\[1.1ex] 6 &amp; 4 &amp; 4 \\\\[1.1ex] 3 &amp; -2 &amp; 1\\end{vmatrix}}{\\begin{vmatrix} A \\end{vmatrix}} = \\cfrac{0}{-6} = \\bm{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"113\" width=\"217\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8ba1\u7b97<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-23aa090e6102a41de5ad5515112e4d03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  z\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u6839\u636e\u514b\u83b1\u9ed8\u89c4\u5219\uff0c\u6211\u4eec\u5c06 A \u884c\u5217\u5f0f\u7684\u7b2c\u4e09\u5217\u66f4\u6539\u4e3a\u72ec\u7acb\u9879\u5217\uff0c\u5e76\u5c06\u5176\u9664\u4ee5 A \u7684\u884c\u5217\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-5bc157a8c4dfe8ee4651affac68ef878_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{z} = \\cfrac{\\begin{vmatrix} -2 &amp; 5 &amp; 8 \\\\[1.1ex] 6 &amp; 2 &amp; 4 \\\\[1.1ex] 3 &amp; -2 &amp; -2\\end{vmatrix}}{\\begin{vmatrix} A \\end{vmatrix}} = \\cfrac{-32}{-8} = \\bm{4}\" title=\"Rendered by QuickLaTeX.com\" height=\"113\" width=\"247\" style=\"vertical-align: 0px;\"><\/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-6c004c5c466235d2d1a784707145d952_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{x =-2 \\qquad y=0 \\qquad z=4}\" 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\u4e605<\/h3>\n<p>\u4f7f\u7528\u514b\u83b1\u9ed8\u6cd5\u5219\u6c42\u89e3\u4ee5\u4e0b\u7ebf\u6027\u65b9\u7a0b\u7ec4\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\/exemple-comment-resoudre-un-systeme-dequations-avec-la-regle-de-cramer.webp\" alt=\"\u4f7f\u7528\u514b\u83b1\u9ed8\u6cd5\u5219\u6c42\u89e3\u65b9\u7a0b\u7ec4\u7684\u793a\u4f8b\" class=\"wp-image-4008\" width=\"215\" height=\"127\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\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\u5236\u4f5c\u7cfb\u7edf\u7684\u77e9\u9635A\u548c\u6269\u5c55\u77e9\u9635A&#8217;\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-f5153b5951b768cc3cafa2bb2567ba92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A= \\left( \\begin{array}{ccc} 3 &amp; -2 &amp; -3 \\\\[1.1ex] -1 &amp; 5 &amp; 4 \\\\[1.1ex] 5 &amp; 1 &amp; -2 \\end{array} \\right) \\qquad A'= \\left( \\begin{array}{ccc|c} 3 &amp; -2 &amp; -3 &amp; 4 \\\\[1.1ex] -1 &amp; 5 &amp; 4 &amp; -10 \\\\[1.1ex] 5 &amp; 1 &amp; -2 &amp; -2 \\end{array}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"455\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u8ba1\u7b97\u77e9\u9635 A \u7684\u8303\u56f4\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-f3778c9499e2a44ea3834dfed1523163_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix}A \\end{vmatrix}= \\begin{vmatrix} 3 &amp; -2 &amp; -3 \\\\[1.1ex] -1 &amp; 5 &amp; 4 \\\\[1.1ex] 5 &amp; 1 &amp; -2 \\end{vmatrix} =-30-40+3+75-12+4=0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"426\" 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-03d70742b14ced92f33963df0c86e92f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} 3 &amp; -2 \\\\[1.1ex] -1 &amp; 5  \\end{vmatrix} = 15- (2)= 13 \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"231\" 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-eded270b78ab3d95ce827e3ea428efb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  rg(A)=2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"76\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e00\u65e6\u6211\u4eec\u77e5\u9053\u4e86\u77e9\u9635 A \u7684\u8303\u56f4\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u8ba1\u7b97\u77e9\u9635 A&#8217; \u7684\u8303\u56f4\u3002\u524d 3 \u5217\u7684\u884c\u5217\u5f0f\u7ed9\u51fa 0\uff0c\u56e0\u6b64\u6211\u4eec\u5c1d\u8bd5\u77e9\u9635 A&#8217; \u4e2d\u5176\u4ed6\u53ef\u80fd\u7684 3\u00d73 \u884c\u5217\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-5bed93d532ae4ccd4649a73662f55f0f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} -2 &amp; -3 &amp; 4 \\\\[1.1ex] 5 &amp; 4 &amp; -10 \\\\[1.1ex]  1 &amp; -2 &amp; -2 \\end{vmatrix} = 0 \\qquad \\begin{vmatrix}3 &amp; -3 &amp; 4 \\\\[1.1ex] -1 &amp; 4 &amp; -10 \\\\[1.1ex] 5 &amp; -2 &amp; -2\\end{vmatrix} = 0 \\qquad \\begin{vmatrix} 3 &amp; -2 &amp; 4 \\\\[1.1ex] -1 &amp; 5 &amp; -10 \\\\[1.1ex] 5 &amp; 1 &amp;-2\\end{vmatrix} = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"535\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6240\u6709 3 \u9636\u884c\u5217\u5f0f\u90fd\u7ed9\u51fa 0\u3002\u4f46\u662f\uff0c\u663e\u7136\uff0c\u77e9\u9635 A&#8217; \u4e0e\u77e9\u9635 A \u5177\u6709\u76f8\u540c\u7684 2 \u9636\u884c\u5217\u5f0f\uff08\u9664\u4e86 0\uff09\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-858d95d7d252b16706b66c0e6aba09c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} 3 &amp; -2 \\\\[1.1ex] -1 &amp; 5 \\end{vmatrix} = 13 \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"145\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u77e9\u9635 A&#8217; \u7684\u79e9\u4e5f\u662f 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-80398cfd2fff647f81c0d4160f3b2f7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  rg(A')=2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"81\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u77e9\u9635 A \u7684\u79e9\u7b49\u4e8e\u77e9\u9635 A&#8217; \u7684\u79e9\uff0c\u4f46\u8fd9\u4e24\u4e2a\u90fd\u5c0f\u4e8e\u7cfb\u7edf\u7684\u672a\u77e5\u6570\u6570 (3)\uff0c\u56e0\u6b64\u6839\u636e<strong>Rouch\u00e9-Frobenius \u5b9a\u7406<\/strong>\u6211\u4eec\u77e5\u9053\u5b83\u662f\u4e00\u4e2a<strong>\u4e0d\u5b9a\u7cfb\u7edf\u517c\u5bb9<\/strong>(SCI) :<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-96868a2569ea0ab5ca99d8dc606d3dc9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{array}{c} \\begin{array}{c} \\color{black}rg(A) = 2 \\\\[1.3ex] \\color{black}rg(A')=2 \\\\[1.3ex] \\color{black}\\text{N\\'umero de inc\\'ognitas} = 3    \\end{array}} \\\\ \\\\  \\color{blue} \\boxed{ \\color{black}\\phantom{^9_9} rg(A) = rg(A') = 2 \\ < \\ n =3  \\color{blue} \\ \\bm{\\longrightarrow} \\ \\color{black} \\bm{SCI}\\phantom{^9_9}} \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"138\" width=\"475\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4f5c\u4e3a\u4e00\u4e2a ICS \u7cfb\u7edf\uff0c\u6211\u4eec\u5fc5\u987b\u6d88\u9664\u4e00\u4e2a\u65b9\u7a0b\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c<strong>\u6211\u4eec\u5c06\u4ece\u7cfb\u7edf\u4e2d\u6d88\u9664\u6700\u540e\u4e00\u4e2a\u65b9\u7a0b<\/strong>\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-4e10bd826663dff41c4272610cbc07b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases} 3x-2y-3z=4 \\\\[1.5ex] -x+5y+4z=-10 \\\\[1.5ex]\\cancel{5x+y-2z = -2} \\end{cases} \\longrightarrow \\quad \\begin{cases} 3x-2y-3z=4 \\\\[1.5ex] -x+5y+4z=-10\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"423\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"><strong>\u73b0\u5728\u8ba9\u6211\u4eec\u5c06\u53d8\u91cf z \u8f6c\u6362\u4e3a \u03bb\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-2502be450040b38761c08e5d6beaf379_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases} 3x-2y-3z=4 \\\\[1.5ex] -x+5y+4z=-10  \\end{cases} \\xrightarrow{z \\ = \\ \\lambda}\\quad \\begin{cases} 3x-2y-3\\lambda=4 \\\\[1.5ex] -x+5y+4\\lambda=-10\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"444\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u5c06\u5e26\u6709 \u03bb \u7684\u9879\u4e0e\u72ec\u7acb\u9879\u653e\u5728\u4e00\u8d77\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-80a43d98e6be30965d554e8a89aa5d89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases} 3x-2y=4+3\\lambda \\\\[1.5ex] -x+5y=-10-4\\lambda\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"172\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4f7f\u5f97\u7cfb\u7edf\u7684\u77e9\u9635A\u548c\u77e9\u9635A&#8217;\u4fdd\u6301\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-3451ce571163983cf41794d4998283d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A= \\left( \\begin{array}{ccc} 3 &amp; -2  \\\\[1.1ex] -1 &amp; 5 \\end{array} \\right) \\qquad A'= \\left( \\begin{array}{cc|c} 3 &amp; -2 &amp; 4+3\\lambda \\\\[1.1ex] 1 &amp; 5 &amp;-10-4\\lambda \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"399\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\uff0c\u4e00\u65e6\u6211\u4eec\u6539\u53d8\u4e86\u7cfb\u7edf\uff0c<strong>\u6211\u4eec\u5c31\u5e94\u7528\u514b\u83b1\u9ed8\u89c4\u5219<\/strong>\u3002\u56e0\u6b64\u6211\u4eec\u6c42\u89e3 A \u7684\u884c\u5217\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-0e7a7d6208ea5e762f5c74a44e6838cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix}A \\end{vmatrix}= \\begin{vmatrix}3&amp; -2 \\\\[1.1ex] -1 &amp; 5\\end{vmatrix} =13\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"162\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8ba1\u7b97\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-757d0eed520b26d08cc3b8b397d0f980_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u6839\u636e\u514b\u83b1\u9ed8\u89c4\u5219\uff0c\u6211\u4eec\u5c06 A \u884c\u5217\u5f0f\u7684\u7b2c\u4e00\u5217\u66f4\u6539\u4e3a\u72ec\u7acb\u9879\u5217\uff0c\u7136\u540e\u5c06\u5176\u9664\u4ee5 A \u7684\u884c\u5217\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-8c30fcc0526c2d4112eb4f60a3d8847f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{x} = \\cfrac{\\begin{vmatrix} 4+3\\lambda &amp; -2 \\\\[1.1ex]-10-4\\lambda &amp; 5\\end{vmatrix}}{\\begin{vmatrix} A \\end{vmatrix}} = \\cfrac{20+15\\lambda -(20+8\\lambda)}{13} = \\cfrac{\\bm{7\\lambda}}{\\bm{13}}\" title=\"Rendered by QuickLaTeX.com\" height=\"81\" width=\"394\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8ba1\u7b97\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-5fb4fb8b1addff607711094fd1ed326e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u6839\u636e\u514b\u83b1\u9ed8\u89c4\u5219\uff0c\u6211\u4eec\u5c06 A \u884c\u5217\u5f0f\u7684\u7b2c\u4e8c\u5217\u66f4\u6539\u4e3a\u72ec\u7acb\u9879\u5217\uff0c\u5e76\u5c06\u5176\u9664\u4ee5 A \u7684\u884c\u5217\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-fdb22a54274e019c811c9051502c474a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{y} = \\cfrac{\\begin{vmatrix} 3 &amp; 4+3\\lambda \\\\[1.1ex] -1 &amp; -10-4\\lambda\\end{vmatrix}}{\\begin{vmatrix} A \\end{vmatrix}} = \\cfrac{-30-12\\lambda -(-4-3\\lambda)}{13}= \\cfrac{\\bm{-26-9\\lambda}}{\\bm{13}}\" title=\"Rendered by QuickLaTeX.com\" height=\"81\" width=\"473\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u65b9\u7a0b\u7ec4\u7684\u89e3\u662f \u03bb \u7684\u51fd\u6570\uff0c\u56e0\u4e3a\u5b83\u662f\u4e00\u4e2a SCI\uff0c\u56e0\u6b64\u8be5\u65b9\u7a0b\u7ec4\u6709\u65e0\u7a77\u591a\u4e2a\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-d0e525b9aca6bd683491ab7950f039e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{x=} \\cfrac{\\bm{7\\lambda}}{\\bm{13}} \\qquad \\bm{y=} \\cfrac{\\bm{-26-9\\lambda}}{\\bm{13}} \\qquad \\bm{z = \\lambda}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"266\" style=\"vertical-align: -12px;\"><\/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\u514b\u83b1\u9ed8\u89c4\u5219\uff0c\u6b64\u5916\uff0c\u60a8\u8fd8\u5c06\u627e\u5230\u901a\u8fc7\u514b\u83b1\u9ed8\u89c4\u5219\u6c42\u89e3\u65b9\u7a0b\u7ec4\u7684\u793a\u4f8b\u548c\u7ec3\u4e60\u3002 \u4ec0\u4e48\u662f\u514b\u83b1\u9ed8\u6cd5\u5219 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/cramer-%e7%9a%84%e8%a7%84%e5%88%99%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\">\u514b\u83b1\u9ed8\u6cd5\u5219<\/span> \u67e5\u770b\u5168\u6587 &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[18],"tags":[],"class_list":["post-298","post","type-post","status-publish","format-standard","hentry","category-18"],"yoast_head":"<!-- This site is optimized 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