{"id":299,"date":"2023-07-06T14:08:28","date_gmt":"2023-07-06T14:08:28","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e5%b8%a6%e5%8f%82%e6%95%b0%e6%96%b9%e7%a8%8b%e7%bb%84%e7%9a%84%e8%ae%a8%e8%ae%ba\/"},"modified":"2023-07-06T14:08:28","modified_gmt":"2023-07-06T14:08:28","slug":"%e5%b8%a6%e5%8f%82%e6%95%b0%e6%96%b9%e7%a8%8b%e7%bb%84%e7%9a%84%e8%ae%a8%e8%ae%ba","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e5%b8%a6%e5%8f%82%e6%95%b0%e6%96%b9%e7%a8%8b%e7%bb%84%e7%9a%84%e8%ae%a8%e8%ae%ba\/","title":{"rendered":"\u5e26\u53c2\u6570\u65b9\u7a0b\u7ec4\u7684\u8ba8\u8bba"},"content":{"rendered":"<p>\u5728\u672c\u9875\u4e2d\uff0c\u6211\u4eec\u5c06\u4e86\u89e3\u5982\u4f55\u8ba8\u8bba\u548c\u6c42\u89e3<strong>\u5e26\u53c2\u6570\u7684\u65b9\u7a0b\u7ec4<\/strong>\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u5c06\u627e\u5230\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u793a\u4f8b\u548c\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u6765\u8fdb\u884c\u7ec3\u4e60\u3002<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u8981\u5206\u6790\u7ebf\u6027\u65b9\u7a0b\u7ec4\uff0c\u4e86\u89e3<a href=\"https:\/\/mathority.org\/cn\/cramer-\u7684\u89c4\u5219\u793a\u4f8b\u548c\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\/\">\u4ec0\u4e48\u662f\u514b\u83b1\u9ed8\u6cd5\u5219<\/a>\u4ee5\u53ca<a href=\"https:\/\/mathority.org\/cn\/\u5fb7\u9c81\u4ec0\u00b7\u5f17\u7f57\u8d1d\u5c3c\u4e4c\u65af\u5b9a\u7406\uff08\u9644\u793a\u4f8b\u548c\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\uff09\/\">\u4ec0\u4e48\u662f\u9c81\u6b47-\u5f17\u7f57\u8d1d\u5c3c\u4e4c\u65af\u5b9a\u7406<\/a>\u975e\u5e38\u91cd\u8981\uff0c\u56e0\u4e3a\u6211\u4eec\u5c06\u4e0d\u65ad\u4f7f\u7528\u5b83\u4eec\u3002<\/p>\n<h2 class=\"wp-block-heading\">\u5e26\u53c2\u6570\u7684\u7ebf\u6027\u65b9\u7a0b\u7ec4\u793a\u4f8b<\/h2>\n<ul>\n<li>\u6839\u636e\u53c2\u6570<em>m<\/em>\u8ba8\u8bba\u5e76\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-6ab2286d15c20029b98a5ea4622033d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases} x+y+2z= 2 \\\\[1.5ex] -x+my+2z=0 \\\\[1.5ex] 3x+mz = 4\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"155\" 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-bef8e6b26595703c77c65178cbf90ffc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A= \\left( \\begin{array}{ccc}1 &amp; 1 &amp; 2 \\\\[1.1ex] -1 &amp; m &amp; 2 \\\\[1.1ex] 3 &amp; 0 &amp; m \\end{array} \\right) \\qquad A'= \\left( \\begin{array}{ccc|c} 1 &amp; 1 &amp; 2 &amp; 2 \\\\[1.1ex] -1 &amp; m &amp; 2 &amp; 0 \\\\[1.1ex] 3 &amp; 0 &amp; m &amp; 4 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"404\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u4f7f\u7528 Sarrus \u89c4\u5219\u6c42\u89e3 A \u7684\u884c\u5217\u5f0f\uff0c\u770b\u770b\u77e9\u9635\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-e823f83f25f798bd854612a7352680d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\begin{aligned}  \\begin{vmatrix}A \\end{vmatrix}= \\begin{vmatrix} 1 &amp; 1 &amp; 2 \\\\[1.1ex] -1 &amp; m &amp; 2 \\\\[1.1ex] 3 &amp; 0 &amp; m \\end{vmatrix} &amp; =m^2+6+0-6m-0+m \\\\ &amp; = m^2-5m+6 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"110\" width=\"366\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64 A \u884c\u5217\u5f0f\u7684\u7ed3\u679c\u53d6\u51b3\u4e8e<em>m<\/em>\u7684\u503c\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5c06\u770b\u5230\u884c\u5217\u5f0f\u5bf9\u4e8e<em>m<\/em>\u7684\u54ea\u4e9b\u503c\u6d88\u5931\u3002\u4e3a\u6b64\uff0c<strong>\u6211\u4eec\u5c06\u7ed3\u679c\u8bbe\u7f6e\u4e3a 0<\/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-a2101d9a1d88f3e3d29bb4758d2fb8a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle   m^2-5m+6 = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"133\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u7528\u4ee5\u4e0b\u516c\u5f0f\u6c42\u89e3\u4e8c\u6b21\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-51910dd69f9df6fdde6dd7597f889700_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  m = \\cfrac{-b \\pm \\sqrt{b^2-4ac}}{2a}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"170\" 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-e863082ac1f9b43df4de9fe93f5eb305_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  m = \\cfrac{-(-5) \\pm \\sqrt{(-5)^2-4\\cdot 1 \\cdot 6}}{2 \\cdot 1} = \\cfrac{5 \\pm \\sqrt{25-24}}{2} =\\cfrac{5 \\pm 1}{2} = \\begin{cases} \\bm{m = 3} \\\\[2ex] \\bm{m =2} \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"537\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6240\u4ee5\u5f53<em>m<\/em>\u7b49\u4e8e2\u62163\u65f6\uff0cA\u7684\u884c\u5217\u5f0f\u5c06\u662f0\u3002\u800c\u5f53<em>m<\/em>\u4e0d\u7b49\u4e8e2\u4e14\u4e0d\u7b49\u4e8e3\u65f6\uff0cA\u7684\u884c\u5217\u5f0f\u5c06\u4e0d\u7b49\u4e8e0\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u6211\u4eec\u5fc5\u987b\u9488\u5bf9\u6bcf\u79cd\u60c5\u51b5\u5206\u522b\u8fdb\u884c\u5206\u6790\uff1a<\/p>\n<p style=\"font-size:26px\"> <span style=\"color:#1976d2;\"><strong>m\u22603 \u548c m\u22602\uff1a<\/strong><\/span><\/p>\n<p>\u6b63\u5982\u6211\u4eec\u521a\u624d\u770b\u5230\u7684\uff0c\u5f53\u53c2\u6570<em>m<\/em>\u4e0d\u7b49\u4e8e 2 \u548c 3 \u65f6\uff0c\u77e9\u9635 A \u7684\u884c\u5217\u5f0f\u4e0d\u7b49\u4e8e 0\u3002\u56e0\u6b64\uff0c <strong>A \u7684\u79e9\u4e3a 3<\/strong> \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-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>\u6b64\u5916\uff0c<strong>\u77e9\u9635 A&#8217; \u7684\u79e9\u4e5f\u662f 3<\/strong> \uff0c\u56e0\u4e3a\u5b83\u5185\u90e8\u6709\u4e00\u4e2a\u884c\u5217\u5f0f\u4e0d\u4e3a 0 \u7684 3\u00d73 \u5b50\u77e9\u9635\u3002\u5e76\u4e14\u5b83\u7684\u79e9\u4e0d\u80fd\u4e3a 4 \uff0c\u56e0\u4e3a\u201c\u6211\u4eec\u65e0\u6cd5\u521b\u5efa 4\u00d74 \u884c\u5217\u5f0f\u201d\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>\u7136\u540e\uff0c\u7531\u4e8e\u77e9\u9635 A \u7684\u79e9\u7b49\u4e8e\u77e9\u9635 A&#8217; \u7684\u79e9\u548c\u7cfb\u7edf\u7684\u672a\u77e5\u6570 (3)\uff0c\u6839\u636e<strong>Rouch\u00e9-Frobenius \u5b9a\u7406<\/strong>\uff0c\u6211\u4eec\u77e5\u9053\u5b83\u662f<strong>\u786e\u5b9a\u517c\u5bb9\u7cfb\u7edf<\/strong>(SCD) :<\/p>\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\u517c\u5bb9\u786e\u5b9a\u7cfb\u7edf\uff08DCS\uff09\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-bef8e6b26595703c77c65178cbf90ffc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A= \\left( \\begin{array}{ccc}1 &amp; 1 &amp; 2 \\\\[1.1ex] -1 &amp; m &amp; 2 \\\\[1.1ex] 3 &amp; 0 &amp; m \\end{array} \\right) \\qquad A'= \\left( \\begin{array}{ccc|c} 1 &amp; 1 &amp; 2 &amp; 2 \\\\[1.1ex] -1 &amp; m &amp; 2 &amp; 0 \\\\[1.1ex] 3 &amp; 0 &amp; m &amp; 4 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"404\" 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-aac47361358555f733a42cffecabdbe9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix}A \\end{vmatrix}= \\begin{vmatrix} 1 &amp; 1 &amp; 2 \\\\[1.1ex] -1 &amp; m &amp; 2 \\\\[1.1ex] 3 &amp; 0 &amp; m \\end{vmatrix} = m^2-5m+6\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"268\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u4e3a\u4e86\u4f7f\u7528\u514b\u83b1\u9ed8\u6cd5\u5219\u8ba1\u7b97 x\uff0c\u6211\u4eec\u5c06\u77e9\u9635 A \u7684\u884c\u5217\u5f0f\u7684\u7b2c\u4e00\u5217\u66f4\u6539\u4e3a\u72ec\u7acb\u9879\u7684\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-b17f49436fdadbb014011b5c461a4a56_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\bm{x} = \\cfrac{\\begin{vmatrix} 2 &amp; 1 &amp; 2\\\\[1.1ex]0&amp;m&amp;2 \\\\[1.1ex] 4 &amp; 0 &amp; m \\end{vmatrix}}{\\begin{vmatrix} A \\end{vmatrix}} = \\cfrac{2m^2+8-8m}{m^2-5m+6}\" title=\"Rendered by QuickLaTeX.com\" height=\"113\" width=\"257\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u4e3a\u4e86\u4f7f\u7528\u514b\u83b1\u9ed8\u6cd5\u5219\u8ba1\u7b97 y\uff0c\u6211\u4eec\u5c06 A \u7684\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-6a2bf75bdabfb2c83870f1869ce19e3d_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; 0 &amp; 2 \\\\[1.1ex] 3 &amp; 4 &amp; m \\end{vmatrix}}{\\begin{vmatrix} A \\end{vmatrix}}=\\cfrac{-4+2m}{m^2-5m+6}\" title=\"Rendered by QuickLaTeX.com\" height=\"113\" width=\"255\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u4e3a\u4e86\u7528\u514b\u83b1\u9ed8\u6cd5\u5219\u8ba1\u7b97 z\uff0c\u6211\u4eec\u5c06 A \u7684\u884c\u5217\u5f0f\u7684\u7b2c\u4e09\u5217\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-eebb3c4d280afc8a9aed8877ddcd4ac5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{z} = \\cfrac{\\begin{vmatrix}  1 &amp; 1 &amp; 2 \\\\[1.1ex] -1 &amp; m &amp; 0 \\\\[1.1ex] 3 &amp; 0 &amp; 4\\end{vmatrix}}{\\begin{vmatrix} A \\end{vmatrix}} = \\cfrac{-2m+4}{m^2-5m+6}\" title=\"Rendered by QuickLaTeX.com\" height=\"113\" width=\"254\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u5bf9\u4e8e m\u22603 \u548c m\u22602 \u7684\u60c5\u51b5\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-7cba73a14f41d3314575e075f1229e87_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{x =} \\cfrac{\\bm{2m^2+8-8m}}{\\bm{m^2-5m+6}} \\qquad \\bm{y=} \\cfrac{\\bm{-4+2m}}{\\bm{m^2-5m+6}} \\qquad \\bm{z =} \\cfrac{\\bm{-2m+4}}{\\bm{m^2-5m+6}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"470\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p>\u6b63\u5982\u60a8\u6240\u770b\u5230\u7684\uff0c\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u65b9\u7a0b\u7ec4\u7684\u89e3\u662f m \u7684\u51fd\u6570\u3002<\/p>\n<p>\u4e00\u65e6\u6211\u4eec\u627e\u5230\u4e86 m \u4e0d\u7b49\u4e8e 2 \u548c 3 \u65f6\u7684\u89e3\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u6c42\u89e3 m \u7b49\u4e8e 2 \u65f6\u7684\u65b9\u7a0b\u7ec4\uff1a<\/p>\n<div class=\"adsb30\" style=\" margin:px; text-align:\"><\/div>\n<p style=\"font-size:26px\"><span style=\"color:#1976d2;\"><strong>\u7c73=2\uff1a<\/strong><\/span><\/p>\n<p>\u73b0\u5728\u6211\u4eec\u5c06\u5206\u6790\u53c2\u6570<em>m<\/em>\u7b49\u4e8e 2 \u65f6\u7684\u7cfb\u7edf\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u77e9\u9635 A \u548c 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-f42ec4801f3e84cd44b4e0b2ae6351cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A= \\left( \\begin{array}{ccc}1 &amp; 1 &amp; 2 \\\\[1.1ex] -1 &amp; 2 &amp; 2 \\\\[1.1ex] 3 &amp; 0 &amp; 2 \\end{array} \\right) \\qquad A'= \\left( \\begin{array}{ccc|c} 1 &amp; 1 &amp; 2 &amp; 2 \\\\[1.1ex] -1 &amp; 2 &amp; 2 &amp; 0 \\\\[1.1ex] 3 &amp; 0 &amp; 2 &amp; 4 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"377\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6b63\u5982\u6211\u4eec\u4e4b\u524d\u770b\u5230\u7684\uff0c\u5f53 m=2 \u65f6\uff0cA \u7684\u884c\u5217\u5f0f\u4e3a 0\u3002\u56e0\u6b64\uff0c\u77e9\u9635 A \u7684\u79e9\u4e0d\u662f 3\u3002\u4f46\u5176\u5185\u90e8\u6709 2\u00d72 \u4e2a\u4e0d\u540c\u4e8e 0 \u7684\u884c\u5217\u5f0f\uff0c\u4f8b\u5982\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-55ef6cd148fca7a869e14760007e1f2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix}1 &amp; 1 \\\\[1.1ex] -1 &amp; 2  \\end{vmatrix} = 2 - (-1)=3 \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"213\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b<strong>\uff0cA \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\u79e9\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u8ba1\u7b97 A&#8217; \u7684\u79e9\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-2c68c742cae37c52ad2566b7feec5301_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} 1 &amp; 2 &amp; 2 \\\\[1.1ex] 2 &amp; 2 &amp; 0 \\\\[1.1ex] 0 &amp; 2 &amp; 4 \\end{vmatrix} = 0 \\qquad \\begin{vmatrix} 1 &amp; 2 &amp; 2 \\\\[1.1ex] -1 &amp; 2 &amp; 0 \\\\[1.1ex] 3 &amp; 2 &amp; 4 \\end{vmatrix}=0\\qquad \\begin{vmatrix} 1 &amp; 1 &amp; 2 \\\\[1.1ex] -1 &amp; 2 &amp; 0 \\\\[1.1ex] 3 &amp; 0 &amp; 4\\end{vmatrix}=0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"412\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u7ef4\u5ea6 3\u00d73 \u7684\u6240\u6709\u53ef\u80fd\u7684\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 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-55ef6cd148fca7a869e14760007e1f2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix}1 &amp; 1 \\\\[1.1ex] -1 &amp; 2  \\end{vmatrix} = 2 - (-1)=3 \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"213\" 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>\u65e2\u7136\u662fICS\uff0c\u5c31\u9700\u8981\u5bf9\u7cfb\u7edf\u8fdb\u884c\u6539\u9020\u6765\u89e3\u51b3\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u5fc5\u987b\u9996\u5148\u4ece\u7cfb\u7edf\u4e2d\u6d88\u9664\u4e00\u4e2a\u65b9\u7a0b\uff0c\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b<strong>\uff0c\u6211\u4eec\u5c06\u5220\u9664\u6700\u540e\u4e00\u4e2a\u65b9\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-10c7facda35cb8894e6bbb236e4953f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases} x+y+2z= 2 \\\\[1.5ex] -x+2y+2z=0 \\\\[1.5ex] \\cancel{3x+2z = 4} \\end{cases} \\longrightarrow \\quad \\begin{cases}  x+y+2z= 2 \\\\[1.5ex] -x+2y+2z=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-0155083595420da31a486927e953805c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases}x+y+2z= 2 \\\\[1.5ex] -x+2y+2z=0  \\end{cases} \\xrightarrow{z \\ = \\ \\lambda}\\quad \\begin{cases} x+y+2\\lambda= 2 \\\\[1.5ex] -x+2y+2\\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-b8486baee4be39f417988ee12b5e67c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases}x+y=2-2\\lambda \\\\[1.5ex] -x+2y=-2\\lambda \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"133\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\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-8591e8c21bce2f49998311bbb08f7dee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A= \\left( \\begin{array}{ccc} 1 &amp; 1  \\\\[1.1ex] -1 &amp; 2 \\end{array} \\right) \\qquad A'= \\left( \\begin{array}{cc|c} 1 &amp; 1 &amp; 2 -2\\lambda \\\\[1.1ex] -1 &amp; 2 &amp; -2\\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\u4e3a\u6b64\uff0c\u6211\u4eec\u9996\u5148\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-c34669d7234c9736c350f793df337bd3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix}A \\end{vmatrix}= \\begin{vmatrix} 1 &amp; 1  \\\\[1.1ex] -1 &amp; 2\\end{vmatrix} =2-(-1)=3\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"229\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u4e3a\u4e86\u4f7f\u7528\u514b\u83b1\u9ed8\u6cd5\u5219\u8ba1\u7b97<em>x<\/em> \uff0c\u6211\u4eec\u5c06 A \u7684\u884c\u5217\u5f0f\u7684\u7b2c\u4e00\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-987ebe052154332042afeb27535996f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{x} = \\cfrac{\\begin{vmatrix} 2 -2\\lambda &amp; 1  \\\\[1.1ex] -2\\lambda &amp; 2 \\end{vmatrix}}{\\begin{vmatrix} A \\end{vmatrix}} = \\cfrac{4-4\\lambda-(-2\\lambda)}{3} = \\cfrac{\\bm{4-2\\lambda}}{\\bm{3}}\" title=\"Rendered by QuickLaTeX.com\" height=\"81\" width=\"345\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u4e3a\u4e86\u4f7f\u7528\u514b\u83b1\u9ed8\u6cd5\u5219\u8ba1\u7b97<em>y<\/em> \uff0c\u6211\u4eec\u5c06 A \u7684\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-8a3c7b2cd7319f7f9db6df7df79abb50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{y} = \\cfrac{\\begin{vmatrix} 1 &amp; 2 -2\\lambda  \\\\[1.1ex] -1 &amp; -2\\lambda  \\end{vmatrix}}{\\begin{vmatrix} A \\end{vmatrix}}=\\cfrac{-2\\lambda -(-2+2\\lambda)}{3} = \\cfrac{\\bm{2-4\\lambda} }{\\bm{3}}\" title=\"Rendered by QuickLaTeX.com\" height=\"81\" width=\"379\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u5f53 m=2 \u65f6\uff0c\u65b9\u7a0b\u7ec4\u7684\u89e3\u662f \u03bb \u7684\u51fd\u6570\uff0c\u56e0\u4e3a\u5b83\u662f SCI\uff0c\u56e0\u6b64\u5b83\u6709\u65e0\u9650\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-1bc871365fab3194e382053fc6b083b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{x =}  \\cfrac{\\bm{4-2\\lambda}}{\\bm{3}}  \\qquad \\bm{y=}\\cfrac{\\bm{2-4\\lambda}}{\\bm{3}} \\qquad \\bm{z=\\lambda}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"274\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u5df2\u7ecf\u5206\u6790\u4e86\u5f53\u53c2\u6570<em>m<\/em>\u4e0d\u7b49\u4e8e 2 \u548c 3 \u4ee5\u53ca\u7b49\u4e8e 2 \u65f6\u7cfb\u7edf\u7684\u89e3\u3002\u56e0\u6b64\u6211\u4eec\u53ea\u9700\u8981\u6700\u540e\u4e00\u79cd\u60c5\u51b5\uff1a\u5f53<em>m<\/em>\u53d6\u503c 3 \u65f6\uff1a <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-118\"><\/div>\n<\/div>\n<p style=\"font-size:26px\"><span style=\"color:#1976d2;\"><strong>\u7c73=3\uff1a<\/strong><\/span><\/p>\n<p>\u73b0\u5728\u6211\u4eec\u5c06\u5206\u6790\u5f53\u53c2\u6570<em>m<\/em>\u4e3a 3 \u65f6\u4f1a\u53d1\u751f\u4ec0\u4e48\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u77e9\u9635 A \u548c 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-c49bbc0d7d36606aa59be050c2682de5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A= \\left( \\begin{array}{ccc}1 &amp; 1 &amp; 2 \\\\[1.1ex] -1 &amp; 3 &amp; 2 \\\\[1.1ex] 3 &amp; 0 &amp; 3 \\end{array} \\right) \\qquad A'= \\left( \\begin{array}{ccc|c} 1 &amp; 1 &amp; 2 &amp; 2 \\\\[1.1ex] -1 &amp; 3 &amp; 2 &amp; 0 \\\\[1.1ex] 3 &amp; 0 &amp; 3 &amp; 4 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"377\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6b63\u5982\u6211\u4eec\u4e4b\u524d\u770b\u5230\u7684\uff0c\u5f53 m=3 \u65f6\uff0cA \u7684\u884c\u5217\u5f0f\u4e3a 0\u3002\u56e0\u6b64\u77e9\u9635 A \u4e0d\u662f 3 \u9636\u7684\u3002\u4f46\u5b83\u5185\u90e8\u6709 2\u00d72 \u4e2a\u4e0d\u540c\u4e8e 0 \u7684\u884c\u5217\u5f0f\uff0c\u4f8b\u5982\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-d88ce42feb4bba9aa74aae98e1062c4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix}1 &amp; 1 \\\\[1.1ex] -1 &amp; 3  \\end{vmatrix} = 3 - (-1)=4 \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"213\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b<strong>\uff0cA \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\u79e9\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u8ba1\u7b97 A&#8217; \u7684\u79e9\u3002\u524d 3 \u5217\u7684\u884c\u5217\u5f0f\u7ed9\u51fa 0\uff0c\u56e0\u6b64\u6211\u4eec\u5c1d\u8bd5\u77e9\u9635 A&#8217; \u5185\u7684\u53e6\u4e00\u4e2a 3\u00d73 \u884c\u5217\u5f0f\uff0c\u4f8b\u5982\u6700\u540e 3 \u5217\u7684\u884c\u5217\u5f0f\uff1a<\/p>\n<p class=\"has-text-align-center\">\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5e6f1a5c155ca004c73e51bdcbe5ece9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} 1 &amp; 2 &amp; 2 \\\\[1.1ex] 3 &amp; 2 &amp; 0 \\\\[1.1ex] 0 &amp; 3 &amp; 4\\end{vmatrix}=2\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"100\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u77e9\u9635 A&#8217; \u786e\u5b9e\u5305\u542b\u4e00\u4e2a\u7ed3\u679c\u4e0d\u4e3a 0 \u7684\u884c\u5217\u5f0f\uff0c\u56e0\u6b64<strong>\u77e9\u9635 A&#8217; \u7684\u79e9\u4e3a 3<\/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-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>\u56e0\u6b64\uff0c\u5f53m=3\u65f6\uff0c\u77e9\u9635A\u7684\u79e9\u4f4e\u4e8e\u77e9\u9635A&#8217;\u7684\u79e9\u3002\u56e0\u6b64\uff0c\u6839\u636e Rouch\u00e9-Frobenius \u5b9a\u7406\uff0c\u6211\u4eec\u63a8\u65ad\u51fa\u8be5\u7cfb\u7edf\u662f\u4e00\u4e2a<strong>\u4e0d\u76f8\u5bb9\u7cfb\u7edf<\/strong>\uff08IS\uff09 <strong>\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-3454f804b63f3cca9bcf08bc93815f90_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')=3 \\\\[1.3ex] \\color{black}\\text{N\\'umero de inc\\'ognitas}=3\\end{array}} \\\\ \\\\  \\color{blue} \\boxed{ \\color{black}\\phantom{^9_9} rg(A)=2 \\ \\neq \\ rg(A') = 3 \\color{blue} \\ \\bm{\\longrightarrow} \\ \\color{black} \\bm{SI}\\phantom{^9_9}} \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"138\" width=\"426\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c<strong>\u5f53 m = 3 \u65f6\uff0c\u65b9\u7a0b\u7ec4\u65e0\u89e3\u3002<\/strong><\/p>\n<h3 class=\"wp-block-heading\">\u793a\u4f8b\u6458\u8981\uff1a<\/h3>\n<p>\u6b63\u5982\u6211\u4eec\u6240\u770b\u5230\u7684\uff0c\u65b9\u7a0b\u7ec4\u7684\u89e3\u53d6\u51b3\u4e8e\u53c2\u6570<em>m<\/em>\u7684\u503c\u3002\u4ee5\u4e0b\u662f\u6240\u6709\u53ef\u80fd\u60c5\u51b5\u7684\u6458\u8981\uff1a <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-32\">\n<div class=\"wp-block-column is-layout-flow\">\n<ul>\n<li> <span style=\"color:#1976d2;font-size:22px\"><strong>m\u22603 \u548c m\u22602\uff1a<\/strong><\/span> <\/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-cf366a55bd307517f94fd8aa00cdf598_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{SCD} \\longrightarrow \\begin{cases} x = \\cfrac{2m^2+8-8m}{m^2-5m+6} \\\\[3.5ex] y =\\cfrac{-4+2m}{m^2-5m+6} \\\\[3.5ex] z = \\cfrac{-2m+4}{m^2-5m+6} \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"171\" width=\"240\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<ul>\n<li><span style=\"color:#1976d2;font-size:22px\"><strong>\u7c73=2\uff1a<\/strong><\/span> <\/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-94002d4f4d866569ed7d6993dd977b81_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{SCI} \\longrightarrow \\begin{cases} x = \\cfrac{4-2\\lambda}{3} \\\\[3.5ex] y= \\cfrac{2-4\\lambda}{3} \\\\[3.5ex] z = \\lambda \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"150\" width=\"175\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<ul>\n<li><span style=\"color:#1976d2;font-size:22px\"><strong>\u7c73=3\uff1a<\/strong><\/span><\/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-9b971789910fd078c90174ed3d662e9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{SI} \\longrightarrow\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"54\" style=\"vertical-align: -1px;\"><\/p>\n<p>\u7cfb\u7edf\u65e0\u89e3\u3002<\/p>\n<\/div>\n<\/div>\n<p>\u8fd9\u91cc\u6211\u4eec\u4f7f\u7528\u9c81\u4ec0\u5b9a\u7406\u548c\u514b\u62c9\u9ed8\u89c4\u5219\u5b8c\u6210\u4e86\u6574\u4e2a\u8fc7\u7a0b\uff0c\u4f46\u662f\u5e26\u53c2\u6570\u7684\u65b9\u7a0b\u7ec4\u4e5f\u53ef\u4ee5\u901a\u8fc7<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\u65b9\u6cd5\uff08\u9644\u7ec3\u4e60\uff09<\/a>\u8ba8\u8bba\u548c\u6c42\u89e3\u3002\u60a8\u53ef\u4ee5\u5728\u94fe\u63a5\u9875\u9762\u4e0a\u4e86\u89e3\u6709\u5173\u6b64\u65b9\u6cd5\u7684\u66f4\u591a\u4fe1\u606f\uff0c\u60a8\u53ef\u4ee5\u5728\u5176\u4e2d\u627e\u5230\u8be5\u8fc7\u7a0b\u7684\u8be6\u7ec6\u8bf4\u660e\u4ee5\u53ca\u793a\u4f8b\u548c\u9010\u6b65\u89e3\u51b3\u7684\u7ec3\u4e60\u3002<\/p>\n<h2 class=\"wp-block-heading\">\u5df2\u89e3\u51b3\u7684\u5e26\u53c2\u6570\u7ebf\u6027\u65b9\u7a0b\u7ec4\u8ba8\u8bba\u95ee\u9898<\/h2>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u8ba8\u8bba\u5e76\u6c42\u89e3\u4ee5\u4e0b\u53c2\u6570\u76f8\u5173\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\/exercice-resolu-de-systemes-dequations-a-parametres.webp\" alt=\"\u5e26\u53c2\u6570\u65b9\u7a0b\u7ec4\u7684\u6c42\u89e3\u7ec3\u4e60\" class=\"wp-image-4014\" width=\"191\" 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-b641845325965882d4aac899246cffb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A= \\left( \\begin{array}{ccc} 4 &amp; -1 &amp; 1 \\\\[1.1ex] 1 &amp; 1 &amp; -3 \\\\[1.1ex] 3 &amp; -2 &amp; -m \\end{array} \\right) \\qquad A'= \\left( \\begin{array}{ccc|c}4 &amp; -1 &amp; 1 &amp; 0 \\\\[1.1ex] 1 &amp; 1 &amp; -3 &amp; 0 \\\\[1.1ex] 3 &amp; -2 &amp; -m &amp; 0\\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"418\" 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-4d36c7cffe0248a2f45cd5871abc6ed5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{aligned}\\begin{vmatrix}A \\end{vmatrix}= \\begin{vmatrix} 4 &amp; -1 &amp; 1 \\\\[1.1ex] 1 &amp; 1 &amp; -3 \\\\[1.1ex] 3 &amp; -2 &amp; -m \\end{vmatrix} &amp; =-4m+9-2-3-24-m \\\\ &amp; =-5m-20 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"381\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> A \u884c\u5217\u5f0f\u7684\u7ed3\u679c\u53d6\u51b3\u4e8e m \u7684\u503c\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5c06\u770b\u5230\u884c\u5217\u5f0f\u5bf9\u4e8e m \u7684\u54ea\u4e9b\u503c\u6d88\u5931\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u5c06\u7ed3\u679c\u7b49\u4e8e 0 \u5e76\u6c42\u89e3\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-e7d065a700c5f2a7f732719be777027f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-5m-20 = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"109\" 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-bc49744634d23cdf0faf446f33487eac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-5m = 20\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"79\" 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-ca8fa07f8716b941295db488a99a6425_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m = \\cfrac{20}{-5} = -4\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"110\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6240\u4ee5\uff0c\u5f53m\u4e3a-4\u65f6\uff0cA\u7684\u884c\u5217\u5f0f\u5c06\u4e3a0\u3002\u800c\u5f53m\u4e0d\u7b49\u4e8e-4\u65f6\uff0cA\u7684\u884c\u5217\u5f0f\u5c06\u4e0d\u540c\u4e8e0\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5fc5\u987b\u5206\u522b\u5206\u6790\u6bcf\u79cd\u60c5\u51b5\uff1a<\/p>\n<p class=\"has-text-align-left\" style=\"font-size:26px\"> <span style=\"color:#1976d2;\"><strong>m\u2260-4\uff1a<\/strong><\/span><\/p>\n<p class=\"has-text-align-left\">\u6b63\u5982\u6211\u4eec\u521a\u624d\u770b\u5230\u7684\uff0c\u5f53\u53c2\u6570m\u4e0d\u7b49\u4e8e-4\u65f6\uff0c\u77e9\u9635A\u7684\u884c\u5217\u5f0f\u4e0d\u7b49\u4e8e0\u3002\u56e0\u6b64\uff0cA\u7684\u79e9\u4e3a3\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-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\">\u6b64\u5916\uff0c\u77e9\u9635 A&#8217; \u7684\u79e9\u4e5f\u662f 3\uff0c\u56e0\u4e3a\u5b83\u5185\u90e8\u6709\u4e00\u4e2a 3\u00d73 \u5b50\u77e9\u9635\uff0c\u5176\u884c\u5217\u5f0f\u4e0d\u4e3a 0\u3002\u800c\u4e14\u5b83\u7684\u79e9\u4e0d\u53ef\u80fd\u662f 4\uff0c\u56e0\u4e3a\u201c\u6211\u4eec\u65e0\u6cd5\u521b\u5efa 4\u00d74 \u884c\u5217\u5f0f\u201d\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\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-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\u7cfb\u7edf\u662f\u4e00\u4e2a SCD\uff0c\u6211\u4eec\u5c31\u5e94\u7528\u514b\u83b1\u9ed8\u89c4\u5219\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-e9e0bd352ad7713a03824ead1239041c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A= \\left( \\begin{array}{ccc} 4 &amp; -1 &amp; 1  \\\\[1.1ex] 1 &amp; 1 &amp; -3 \\\\[1.1ex] 3 &amp; -2 &amp; -m \\end{array} \\right) \\qquad A'= \\left( \\begin{array}{ccc|c} 4 &amp; -1 &amp; 1 &amp; 0 \\\\[1.1ex] 1 &amp; 1 &amp; -3 &amp; 0 \\\\[1.1ex] 3 &amp; -2 &amp; -m &amp; 0\\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"418\" 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-530cb4576ee1a91d6246ed6cf9dd0fc8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix}A \\end{vmatrix}= \\begin{vmatrix} 4 &amp; -1 &amp; 1  \\\\[1.1ex] 1 &amp; 1 &amp; -3 \\\\[1.1ex] 3 &amp; -2 &amp; -m\\end{vmatrix} =-5m-20\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"253\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8981\u4f7f\u7528\u514b\u83b1\u9ed8\u89c4\u5219\u8ba1\u7b97 xatex]\uff0c\u6211\u4eec\u5c06 A \u884c\u5217\u5f0f\u7684\u7b2c\u4e00\u5217\u66f4\u6539\u4e3a\u72ec\u7acb\u9879\u5217\uff0c\u5e76\u5c06\u5176\u9664\u4ee5 A \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-b076bbda8d086abedb459570d74c80a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{x} = \\cfrac{\\begin{vmatrix} 0 &amp; -1 &amp; 1  \\\\[1.1ex] 0 &amp; 1 &amp; -3 \\\\[1.1ex] 0 &amp; -2 &amp; -m\\end{vmatrix}}{\\begin{vmatrix} A \\end{vmatrix}} = \\cfrac{0}{-5m-20} = \\bm{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"113\" width=\"280\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u8ba1\u7b97\u672a\u77e5\u6570\u5e76\u6839\u636e\u514b\u83b1\u9ed8\u6cd5\u5219\uff0c\u6211\u4eec\u5c06 A \u884c\u5217\u5f0f\u7684\u7b2c\u4e8c\u5217\u66f4\u6539\u4e3a\u72ec\u7acb\u9879\u5217\uff0c\u7136\u540e\u5c06\u5176\u9664\u4ee5 A \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-f642a8cb2fd174e5c383a4df53e11a2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{y} = \\cfrac{\\begin{vmatrix} 4 &amp; 0 &amp; 1  \\\\[1.1ex] 1 &amp; 0 &amp; -3 \\\\[1.1ex] 3 &amp; 0 &amp; -m \\end{vmatrix}}{\\begin{vmatrix} A \\end{vmatrix}} = \\cfrac{0}{-5m-20} = \\bm{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"113\" width=\"265\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u7528\u514b\u83b1\u9ed8\u6cd5\u5219\u8ba1\u7b97 z\uff0c\u6211\u4eec\u5c06 A \u7684\u884c\u5217\u5f0f\u7684\u7b2c\u4e09\u5217\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-5020a9ba4995b9715d8d1fb4720952b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{z} = \\cfrac{\\begin{vmatrix}4 &amp; -1 &amp; 0 \\\\[1.1ex] 1 &amp; 1 &amp; 0 \\\\[1.1ex] 3 &amp; -2 &amp; 0 \\end{vmatrix}}{\\begin{vmatrix} A \\end{vmatrix}} = \\cfrac{0}{-5m-20} = \\bm{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"113\" width=\"258\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0cm\u2260-4\u60c5\u51b5\u4e0b\u65b9\u7a0b\u7ec4\u7684\u89e3\u4e3a\uff1a<\/p>\n<p class=\"has-text-align-center\"> <strong>x=0 y=0 z=0<\/strong><\/p>\n<p class=\"has-text-align-left\" style=\"font-size:26px\"><span style=\"color:#1976d2;\"><strong>\u7c73=-4\uff1a<\/strong><\/span><\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u5c06\u5206\u6790\u53c2\u6570 m \u4e3a -4 \u65f6\u7684\u7cfb\u7edf\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u77e9\u9635 A \u548c A&#8217; \u662f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e585e6465d27ea27ccc2c1a6ec1fe9ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A= \\left( \\begin{array}{ccc} 4 &amp; -1 &amp; 1 \\\\[1.1ex] 1 &amp; 1 &amp; -3 \\\\[1.1ex] 3 &amp; -2 &amp; 4 \\end{array} \\right) \\qquad A'= \\left( \\begin{array}{ccc|c}4 &amp; -1 &amp; 1 &amp; 0 \\\\[1.1ex] 1 &amp; 1 &amp; -3 &amp; 0 \\\\[1.1ex] 3 &amp; -2 &amp; 4 &amp; 0\\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"405\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6b63\u5982\u6211\u4eec\u4e4b\u524d\u770b\u5230\u7684\uff0c\u5f53 m=-4 \u65f6\uff0cA \u7684\u884c\u5217\u5f0f\u4e3a 0\u3002\u56e0\u6b64\uff0c\u77e9\u9635 A \u4e0d\u662f 3 \u9636\u7684\u3002\u4f46\u5b83\u5185\u90e8\u6709 2\u00d72 \u4e2a\u4e0d\u540c\u4e8e 0 \u7684\u884c\u5217\u5f0f\uff0c\u4f8b\u5982\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-a62d150aef4ec798814d25c988b0afd7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle   \\begin{vmatrix}4 &amp; -1 \\\\[1.1ex] 1 &amp; 1 \\end{vmatrix} =4-(-1)=5 \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"213\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7531\u4e8e\u8be5\u77e9\u9635\u5177\u6709\u4e0d\u540c\u4e8e 0 \u7684 2 \u9636\u884c\u5217\u5f0f\uff0c\u56e0\u6b64\u77e9\u9635 A \u7684\u79e9\u4e3a 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-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\u6211\u4eec\u5df2\u7ecf\u77e5\u9053\u524d 3 \u5217\u7684\u884c\u5217\u5f0f\u7ed9\u51fa 0\uff0c\u56e0\u6b64\u6211\u4eec\u5c1d\u8bd5\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-39fc49c7a63920c8956703a4851ecfc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} -1 &amp; 1 &amp; 0 \\\\[1.1ex] 1 &amp; -3 &amp; 0 \\\\[1.1ex]  -2 &amp; 4 &amp; 0 \\end{vmatrix} = 0 \\quad \\begin{vmatrix}4 &amp; 1 &amp; 0 \\\\[1.1ex] 1 &amp;  -3 &amp; 0 \\\\[1.1ex] 3 &amp;  4 &amp; 0  \\end{vmatrix} = 0 \\quad \\begin{vmatrix}4 &amp; -1 &amp;  0 \\\\[1.1ex] 1 &amp; 1 &amp; 0 \\\\[1.1ex] 3 &amp; -2 &amp;  0\\end{vmatrix} = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"404\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u77e9\u9635 A&#8217; \u7684\u6240\u6709 3\u00d73 \u884c\u5217\u5f0f\u5747\u4e3a 0\uff0c\u56e0\u6b64\u77e9\u9635 A&#8217; \u4e5f\u4e0d\u4f1a\u662f 3 \u9636\u7684\u3002\u7136\u800c\uff0c\u5b83\u5185\u90e8\u786e\u5b9e\u6709\u4e0d\u540c\u4e8e 0 \u7684 2 \u9636\u884c\u5217\u5f0f\u3002\u4f8b\u5982\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-a62d150aef4ec798814d25c988b0afd7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle   \\begin{vmatrix}4 &amp; -1 \\\\[1.1ex] 1 &amp; 1 \\end{vmatrix} =4-(-1)=5 \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"213\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\u77e9\u9635 A&#8217; \u7684\u79e9\u4e3a 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\u8303\u56f4\u7b49\u4e8e\u77e9\u9635 A&#8217; \u7684\u8303\u56f4\uff0c\u4f46\u8fd9\u4e24\u8005\u5747\u5c0f\u4e8e\u7cfb\u7edf (3) \u4e2d\u7684\u672a\u77e5\u6570\u6570\u91cf\uff0c\u56e0\u6b64\uff0c\u6839\u636e Rouch\u00e9-Frobenius \u5b9a\u7406\uff0cc \u662f\u4e0d\u5b9a\u76f8\u5bb9\u7cfb\u7edf (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-f43fdf4978386c61d18f9bb5b5883881_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\">\u8fd9\u662f\u4e00\u4e2aICS\u7cfb\u7edf\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u5bf9\u7cfb\u7edf\u8fdb\u884c\u6539\u9020\u6765\u89e3\u51b3\u5b83\u3002\u6211\u4eec\u9996\u5148\u6d88\u9664\u4e00\u4e2a\u65b9\u7a0b\uff0c\u5728\u672c\u4f8b\u4e2d\u8fd9\u5c06\u662f\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-4d5499fda37d3cbf56fbf6ecbfc6bfba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases} 4x-y+z= 0 \\\\[1.5ex] x+y-3z=0 \\\\[1.5ex] \\cancel{3x-2y+4z = 0} \\end{cases} \\longrightarrow \\quad \\begin{cases} 4x-y+z= 0 \\\\[1.5ex] x+y-3z=0\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"349\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u8ba9\u6211\u4eec\u5c06\u53d8\u91cf z \u8f6c\u6362\u4e3a \u03bb\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-96ea68274b072531365282e01d926718_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases}4x-y+z= 0 \\\\[1.5ex] x+y-3z=0 \\end{cases} \\xrightarrow{z \\ = \\ \\lambda}\\quad \\begin{cases} 4x-y+\\lambda= 0 \\\\[1.5ex] x+y-3\\lambda=0\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"353\" 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-6192715e62cc8e3d3fe4c51da8629c70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases} 4x-y=-\\lambda \\\\[1.5ex] x+y=3\\lambda \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"110\" 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 class=\"has-text-align-center\">\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-99a91208ff1742f81e799aa5ab7f9097_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A= \\left( \\begin{array}{ccc} 4 &amp; -1 \\\\[1.1ex] 1 &amp; 1 \\end{array} \\right) \\qquad A'= \\left( \\begin{array}{cc|c} 4 &amp; -1 &amp; -\\lambda \\\\[1.1ex] 1 &amp; 1 &amp; 3\\lambda \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"337\" 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\u6211\u4eec\u5c31\u5e94\u7528\u514b\u83b1\u9ed8\u89c4\u5219\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u9996\u5148\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-34832b783ddaf4af205302240d0feafb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix}A \\end{vmatrix}= \\begin{vmatrix} 4 &amp; -1 \\\\[1.1ex] 1 &amp; 1 \\end{vmatrix} = 4-(-1)=5\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"228\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u4f7f\u7528\u514b\u83b1\u9ed8\u6cd5\u5219\u8ba1\u7b97 x\uff0c\u6211\u4eec\u5c06 A \u7684\u884c\u5217\u5f0f\u7684\u7b2c\u4e00\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-362167d2eaa02d7243dedd5c385d08b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{x} = \\cfrac{\\begin{vmatrix}-\\lambda &amp; -1 \\\\[1.1ex] 3\\lambda &amp; 1 \\end{vmatrix}}{\\begin{vmatrix} A \\end{vmatrix}} = \\cfrac{-\\lambda-(-3\\lambda)}{5} =\\cfrac{\\bm{2\\lambda}}{\\bm{5}}\" title=\"Rendered by QuickLaTeX.com\" height=\"81\" width=\"285\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u8ba1\u7b97\u672a\u77e5\u6570\u5e76\u6839\u636e\u514b\u83b1\u9ed8\u6cd5\u5219\uff0c\u6211\u4eec\u5c06 A \u884c\u5217\u5f0f\u7684\u7b2c\u4e8c\u5217\u66f4\u6539\u4e3a\u72ec\u7acb\u9879\u5217\uff0c\u7136\u540e\u5c06\u5176\u9664\u4ee5 A \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-ede5a3a87ac0bb9ceea4232ec7b381fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{y} = \\cfrac{\\begin{vmatrix} 4 &amp; -\\lambda \\\\[1.1ex] 1 &amp; 3\\lambda \\end{vmatrix}}{\\begin{vmatrix} A \\end{vmatrix}} = \\cfrac{12\\lambda-(-\\lambda)}{5}=\\cfrac{\\bm{13\\lambda}}{\\bm{5}}\" title=\"Rendered by QuickLaTeX.com\" height=\"81\" width=\"267\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u5f53 m=-4 \u65f6\uff0c\u65b9\u7a0b\u7ec4\u7684\u89e3\u662f \u03bb \u7684\u51fd\u6570\uff0c\u56e0\u4e3a\u5b83\u662f SCI\uff0c\u56e0\u6b64\u5177\u6709\u65e0\u9650\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-316aed1af52eba51058c3c753717c1af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{x =}\\cfrac{\\bm{2\\lambda}}{\\bm{5}}\\qquad \\bm{y=}\\cfrac{\\bm{13\\lambda}}{\\bm{5}} \\qquad \\bm{z=\\lambda}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"222\" style=\"vertical-align: -12px;\"><\/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\u4e602<\/h3>\n<p>\u8ba8\u8bba\u5e76\u6c42\u51fa\u4ee5\u4e0b\u53c2\u6570\u76f8\u5173\u7ebf\u6027\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-etape-par-etape-d-un-systeme-d-equations-lineaires-avec-parametres.webp\" alt=\"\u7ec3\u4e60\u9010\u6b65\u6c42\u89e3\u5e26\u53c2\u6570\u7684\u7ebf\u6027\u65b9\u7a0b\u7ec4\" class=\"wp-image-4020\" width=\"187\" height=\"122\" 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-e924dd1b3fe5c0da561b92da9bf5da3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A= \\left( \\begin{array}{ccc} m &amp; 2 &amp; 1 \\\\[1.1ex] 2 &amp; 4 &amp; 2 \\\\[1.1ex] 1 &amp; -2 &amp; m\\end{array} \\right) \\qquad A'= \\left( \\begin{array}{ccc|c}m &amp; 2 &amp; 1 &amp; 2 \\\\[1.1ex] 2 &amp; 4 &amp; 2 &amp; 0 \\\\[1.1ex] 1 &amp; -2 &amp; m &amp; 3\\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"404\" 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-5d0f8dbb7408ac6521e0144ac2f3a8a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{aligned}\\begin{vmatrix}A \\end{vmatrix}= \\begin{vmatrix}m &amp; 2 &amp; 1 \\\\[1.1ex] 2 &amp; 4 &amp; 2 \\\\[1.1ex] 1 &amp; -2 &amp; m\\end{vmatrix} &amp; =4m^2+4-4-4+4m-4m \\\\ &amp; =4m^2-4 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"384\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> A \u884c\u5217\u5f0f\u7684\u7ed3\u679c\u53d6\u51b3\u4e8e m \u7684\u503c\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5c06\u770b\u5230\u884c\u5217\u5f0f\u5bf9\u4e8e m \u7684\u54ea\u4e9b\u503c\u6d88\u5931\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u5c06\u7ed3\u679c\u7b49\u4e8e 0 \u5e76\u6c42\u89e3\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-059d7760bb8cee65e13e43a97e156e1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4m^2-4 = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"95\" 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-1aae0b3268b7d9e348b8eb80ce957ce8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4m^2=4\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"65\" 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-1f31504086ef5ec070b337db57ad444f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m^2 = \\cfrac{4}{4}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"58\" 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-baf4ba1311e2f2ce47aecfb90a411b64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m^2 = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"55\" 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-c8dda3f9896a1a4dece5059a485cdcfb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m = \\pm 1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"61\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u5f53m\u4e3a+1\u6216-1\u65f6\uff0cA\u7684\u884c\u5217\u5f0f\u5c06\u4e3a0\u3002\u800c\u5f53m\u4e0d\u540c\u4e8e+1\u548c-1\u65f6\uff0cA\u7684\u884c\u5217\u5f0f\u5c06\u4e0d\u540c\u4e8e0\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5fc5\u987b\u901a\u8fc7\u4ee5\u4e0b\u65b9\u5f0f\u5206\u6790\u6bcf\u79cd\u60c5\u51b5\uff1a<\/p>\n<p class=\"has-text-align-left\" style=\"font-size:26px\"> <span style=\"color:#1976d2;\"><strong>m\u2260+1 \u4e14 m\u2260-1\uff1a<\/strong><\/span><\/p>\n<p class=\"has-text-align-left\">\u6b63\u5982\u6211\u4eec\u521a\u624d\u770b\u5230\u7684\uff0c\u5f53\u53c2\u6570m\u4e0d\u7b49\u4e8e+1\u548c-1\u65f6\uff0c\u77e9\u9635A\u7684\u884c\u5217\u5f0f\u4e0d\u7b49\u4e8e0\u3002\u56e0\u6b64\uff0cA\u7684\u79e9\u4e3a3\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-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\">\u6b64\u5916\uff0c\u77e9\u9635 A&#8217; \u7684\u79e9\u4e5f\u662f 3\uff0c\u56e0\u4e3a\u5b83\u5185\u90e8\u6709\u4e00\u4e2a 3\u00d73 \u5b50\u77e9\u9635\uff0c\u5176\u884c\u5217\u5f0f\u4e0d\u4e3a 0\u3002\u800c\u4e14\u5b83\u7684\u79e9\u4e0d\u53ef\u80fd\u662f 4\uff0c\u56e0\u4e3a\u201c\u6211\u4eec\u65e0\u6cd5\u521b\u5efa 4\u00d74 \u884c\u5217\u5f0f\u201d\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\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-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\u7cfb\u7edf\u662f\u4e00\u4e2a SCD\uff0c\u6211\u4eec\u5c31\u5e94\u7528\u514b\u83b1\u9ed8\u89c4\u5219\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-e924dd1b3fe5c0da561b92da9bf5da3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A= \\left( \\begin{array}{ccc} m &amp; 2 &amp; 1 \\\\[1.1ex] 2 &amp; 4 &amp; 2 \\\\[1.1ex] 1 &amp; -2 &amp; m\\end{array} \\right) \\qquad A'= \\left( \\begin{array}{ccc|c}m &amp; 2 &amp; 1 &amp; 2 \\\\[1.1ex] 2 &amp; 4 &amp; 2 &amp; 0 \\\\[1.1ex] 1 &amp; -2 &amp; m &amp; 3\\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"404\" 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-b5114be5e37d2c91f02f22fba22edc42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix}A \\end{vmatrix}= \\begin{vmatrix}m &amp; 2 &amp; 1 \\\\[1.1ex] 2 &amp; 4 &amp; 2 \\\\[1.1ex] 1 &amp; -2 &amp; m\\end{vmatrix}=4m^2-4\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"231\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u4f7f\u7528\u514b\u83b1\u9ed8\u6cd5\u5219\u8ba1\u7b97 x\uff0c\u6211\u4eec\u5c06 A \u7684\u884c\u5217\u5f0f\u7684\u7b2c\u4e00\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-4b7402e02ee62bd78a6f880d3d122119_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{x} = \\cfrac{\\begin{vmatrix} 2&amp; 2 &amp; 1 \\\\[1.1ex] 0 &amp; 4 &amp; 2 \\\\[1.1ex] 3 &amp; -2 &amp; m\\end{vmatrix}}{\\begin{vmatrix} A \\end{vmatrix}} = \\cfrac{\\bm{8m+8}}{\\bm{4m^2-4}}\" title=\"Rendered by QuickLaTeX.com\" height=\"113\" width=\"218\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u8ba1\u7b97\u672a\u77e5\u6570\u5e76\u6839\u636e\u514b\u83b1\u9ed8\u6cd5\u5219\uff0c\u6211\u4eec\u5c06 A \u884c\u5217\u5f0f\u7684\u7b2c\u4e8c\u5217\u66f4\u6539\u4e3a\u72ec\u7acb\u9879\u5217\uff0c\u7136\u540e\u5c06\u5176\u9664\u4ee5 A \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-551c66a9530d0195a9a4ff64d42350c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{y} = \\cfrac{\\begin{vmatrix} m &amp; 2 &amp; 1 \\\\[1.1ex] 2 &amp; 0 &amp; 2 \\\\[1.1ex] 1 &amp; 3 &amp; m\\end{vmatrix}}{\\begin{vmatrix} A \\end{vmatrix}} = \\cfrac{\\bm{-10m+10}}{\\bm{4m^2-4}}\" title=\"Rendered by QuickLaTeX.com\" height=\"113\" width=\"235\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u7528\u514b\u83b1\u9ed8\u6cd5\u5219\u8ba1\u7b97 z\uff0c\u6211\u4eec\u5c06 A \u7684\u884c\u5217\u5f0f\u7684\u7b2c\u4e09\u5217\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-28375ce522b7644a745a9adea4c78ae7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{z} = \\cfrac{\\begin{vmatrix}m &amp; 2 &amp; 2 \\\\[1.1ex] 2 &amp; 4 &amp; 0 \\\\[1.1ex] 1 &amp; -2 &amp; 3 \\end{vmatrix}}{\\begin{vmatrix} A \\end{vmatrix}} = \\cfrac{\\bm{12m-28}}{\\bm{4m^2-4}}\" title=\"Rendered by QuickLaTeX.com\" height=\"113\" width=\"227\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u5bf9\u4e8e m\u2260+1 \u548c m\u2260-1 \u7684\u60c5\u51b5\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-59ecb2f1448989cd1c41af45e7bc4a32_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{x = }\\cfrac{\\bm{8m+8}}{\\bm{4m^2-4}} \\qquad \\bm{y=}\\cfrac{\\bm{-10m+10}}{\\bm{4m^2-4}}\\qquad \\bm{z =} \\cfrac{\\bm{12m-28}}{\\bm{4m^2-4}}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"383\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\"font-size:26px\"><span style=\"color:#1976d2;\"><strong>\u7c73=+1\uff1a<\/strong><\/span><\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u5c06\u5206\u6790\u53c2\u6570 m \u7b49\u4e8e 1 \u65f6\u7684\u7cfb\u7edf\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u77e9\u9635 A \u548c 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-f6af272a99ed7c281ee8dd9199698686_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A= \\left( \\begin{array}{ccc} 1 &amp; 2 &amp; 1 \\\\[1.1ex] 2 &amp; 4 &amp; 2 \\\\[1.1ex] 1 &amp; -2 &amp; 1 \\end{array} \\right) \\qquad A'= \\left( \\begin{array}{ccc|c}1 &amp; 2 &amp; 1 &amp; 2 \\\\[1.1ex] 2 &amp; 4 &amp; 2 &amp; 0 \\\\[1.1ex] 1 &amp; -2 &amp; 1 &amp; 3\\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\">\u6b63\u5982\u6211\u4eec\u4e4b\u524d\u770b\u5230\u7684\uff0c\u5f53 m=+1 \u65f6\uff0cA \u7684\u884c\u5217\u5f0f\u4e3a 0\u3002\u56e0\u6b64\u77e9\u9635 A \u4e0d\u662f 3 \u9636\u7684\u3002\u4f46\u5b83\u5185\u90e8\u6709 2\u00d72 \u4e2a\u4e0d\u540c\u4e8e 0 \u7684\u884c\u5217\u5f0f\uff0c\u4f8b\u5982\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-ebedf6c9e4316844dc99ceca9472fac5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle   \\begin{vmatrix}2 &amp; 4\\\\[1.1ex] 1 &amp; -2 \\end{vmatrix} =-4-4=-8 \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"213\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7531\u4e8e\u8be5\u77e9\u9635\u5177\u6709\u4e0d\u540c\u4e8e 0 \u7684 2 \u9636\u884c\u5217\u5f0f\uff0c\u56e0\u6b64\u77e9\u9635 A \u7684\u79e9\u4e3a 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-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\u6211\u4eec\u5df2\u7ecf\u77e5\u9053\u524d 3 \u5217\u7684\u884c\u5217\u5f0f\u7ed9\u51fa 0\uff0c\u6240\u4ee5\u73b0\u5728\u6211\u4eec\u5c1d\u8bd5\u4f7f\u7528\u6700\u540e 3 \u5217\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-4d0109b155be9f87a0cee337ddec5517_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} 2 &amp; 1 &amp; 2 \\\\[1.1ex] 4 &amp; 2 &amp; 0 \\\\[1.1ex]  -2 &amp; 1 &amp; 3 \\end{vmatrix} = 16\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"124\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u53e6\u4e00\u65b9\u9762\uff0c\u77e9\u9635 A&#8217; \u786e\u5b9e\u5305\u542b\u4e00\u4e2a 3\u00d73 \u884c\u5217\u5f0f\uff0c\u5176\u7ed3\u679c\u4e0d\u4e3a 0\uff0c\u56e0\u6b64\u77e9\u9635 A&#8217; \u7684\u79e9\u4e3a 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\u5f53m=+1\u65f6\uff0c\u77e9\u9635A\u7684\u79e9\u5c0f\u4e8e\u77e9\u9635A&#8217;\u7684\u79e9\u3002\u56e0\u6b64\uff0c\u6839\u636e Rouch\u00e9-Frobenius \u5b9a\u7406\uff0c\u6211\u4eec\u63a8\u65ad\u51fa\u8be5\u7cfb\u7edf\u662f\u4e00\u4e2a\u4e0d\u76f8\u5bb9\u7cfb\u7edf\uff08IS\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-b2bb3fec88cf5c6d788afb4480ab1f58_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')=3 \\\\[1.3ex] \\color{black}\\text{N\\'umero de inc\\'ognitas} = 3 \\end{array}} \\\\ \\\\ \\color{blue} \\boxed{ \\color{black}\\phantom{^9_9} rg(A) = 2 \\ \\neq \\ rg(A') = 3 \\color{blue} \\ \\bm{\\longrightarrow} \\ \\color{black} \\bm{SI}\\phantom{^9_9}} \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"138\" width=\"426\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c<strong>\u5f53 m=+1 \u65f6\uff0c\u65b9\u7a0b\u7ec4\u65e0\u89e3<\/strong>\uff0c\u56e0\u4e3a\u5b83\u662f\u4e00\u4e2a\u4e0d\u76f8\u5bb9\u7cfb\u7edf\u3002<\/p>\n<p class=\"has-text-align-left\" style=\"font-size:26px\"><span style=\"color:#1976d2;\"><strong>\u7c73=-1\uff1a<\/strong><\/span><\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u5c06\u5206\u6790\u53c2\u6570 m \u4e3a -1 \u65f6\u7684\u7cfb\u7edf\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u77e9\u9635 A \u548c A&#8217; \u662f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-46b0a00ef38d0e5a433b418de7eb1ec3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A= \\left( \\begin{array}{ccc} -1 &amp; 2 &amp; 1 \\\\[1.1ex] 2 &amp; 4 &amp; 2 \\\\[1.1ex] 1 &amp; -2 &amp; -1 \\end{array} \\right) \\qquad A'= \\left( \\begin{array}{ccc|c}-1 &amp; 2 &amp; 1 &amp; 2 \\\\[1.1ex] 2 &amp; 4 &amp; 2 &amp; 0 \\\\[1.1ex] 1 &amp; -2 &amp; -1 &amp; 3\\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\">\u6b63\u5982\u6211\u4eec\u4e4b\u524d\u770b\u5230\u7684\uff0c\u5f53 m=-1 \u65f6\uff0cA \u7684\u884c\u5217\u5f0f\u4e3a 0\u3002\u56e0\u6b64\uff0c\u77e9\u9635 A \u4e0d\u662f 3 \u9636\u7684\u3002\u4f46\u5b83\u5185\u90e8\u6709 2\u00d72 \u4e2a\u4e0d\u540c\u4e8e 0 \u7684\u884c\u5217\u5f0f\uff0c\u4f8b\u5982\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-ff5373c7e7901f253421efbbd52d192e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle   \\begin{vmatrix}-1 &amp; 2\\\\[1.1ex] 2 &amp; 4 \\end{vmatrix} =-4-4=-8 \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"213\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7531\u4e8e\u8be5\u77e9\u9635\u5177\u6709\u4e0d\u540c\u4e8e 0 \u7684 2 \u9636\u884c\u5217\u5f0f\uff0c\u56e0\u6b64\u77e9\u9635 A \u7684\u79e9\u4e3a 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-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\u6211\u4eec\u5df2\u7ecf\u77e5\u9053\u524d 3 \u5217\u7684\u884c\u5217\u5f0f\u7ed9\u51fa 0\uff0c\u6240\u4ee5\u73b0\u5728\u6211\u4eec\u5c1d\u8bd5\u4f7f\u7528\u7b2c 1\u30013 \u548c 4 \u5217\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-a95e30910bd64db920f3c2bcb5f2ff62_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} -1 &amp; 1 &amp; 2 \\\\[1.1ex] 2 &amp; 2 &amp; 0 \\\\[1.1ex] 1 &amp;  -1 &amp; 3\\end{vmatrix} = -20\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"152\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u53e6\u4e00\u65b9\u9762\uff0c\u77e9\u9635 A&#8217; \u786e\u5b9e\u5305\u542b\u4e00\u4e2a 3\u00d73 \u884c\u5217\u5f0f\uff0c\u5176\u7ed3\u679c\u4e0d\u4e3a 0\uff0c\u56e0\u6b64\u77e9\u9635 A&#8217; \u7684\u79e9\u4e3a 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\u5f53m=-1\u65f6\uff0c\u77e9\u9635A\u7684\u79e9\u4f4e\u4e8e\u77e9\u9635A&#8217;\u7684\u79e9\u3002\u56e0\u6b64\uff0c\u6839\u636e Rouch\u00e9-Frobenius \u5b9a\u7406\uff0c\u6211\u4eec\u63a8\u65ad\u51fa\u8be5\u7cfb\u7edf\u662f\u4e00\u4e2a\u4e0d\u76f8\u5bb9\u7cfb\u7edf\uff08IS\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-b2bb3fec88cf5c6d788afb4480ab1f58_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')=3 \\\\[1.3ex] \\color{black}\\text{N\\'umero de inc\\'ognitas} = 3 \\end{array}} \\\\ \\\\ \\color{blue} \\boxed{ \\color{black}\\phantom{^9_9} rg(A) = 2 \\ \\neq \\ rg(A') = 3 \\color{blue} \\ \\bm{\\longrightarrow} \\ \\color{black} \\bm{SI}\\phantom{^9_9}} \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"138\" width=\"426\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c<strong>\u5f53 m=-1 \u65f6\uff0c\u65b9\u7a0b\u7ec4\u65e0\u89e3<\/strong>\uff0c\u56e0\u4e3a\u5b83\u662f\u4e0d\u76f8\u5bb9\u7cfb\u7edf\u3002<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end 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