{"id":297,"date":"2023-07-06T14:52:33","date_gmt":"2023-07-06T14:52:33","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e5%be%b7%e9%b2%81%e4%bb%80%c2%b7%e5%bc%97%e7%bd%97%e8%b4%9d%e5%b0%bc%e4%b9%8c%e6%96%af%e5%ae%9a%e7%90%86%ef%bc%88%e9%99%84%e7%a4%ba%e4%be%8b%e5%92%8c%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%9a%84%e7%bb%83\/"},"modified":"2023-07-06T14:52:33","modified_gmt":"2023-07-06T14:52:33","slug":"%e5%be%b7%e9%b2%81%e4%bb%80%c2%b7%e5%bc%97%e7%bd%97%e8%b4%9d%e5%b0%bc%e4%b9%8c%e6%96%af%e5%ae%9a%e7%90%86%ef%bc%88%e9%99%84%e7%a4%ba%e4%be%8b%e5%92%8c%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%9a%84%e7%bb%83","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e5%be%b7%e9%b2%81%e4%bb%80%c2%b7%e5%bc%97%e7%bd%97%e8%b4%9d%e5%b0%bc%e4%b9%8c%e6%96%af%e5%ae%9a%e7%90%86%ef%bc%88%e9%99%84%e7%a4%ba%e4%be%8b%e5%92%8c%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%9a%84%e7%bb%83\/","title":{"rendered":"\u9c81\u4ec0-\u5f17\u96f7\u8d1d\u5c3c\u4e4c\u65af\u5b9a\u7406"},"content":{"rendered":"<p>\u5728\u672c\u9875\u4e2d\uff0c\u6211\u4eec\u5c06\u4e86\u89e3\u4ec0\u4e48\u662f<strong>Rouch\u00e9 Frobenius \u5b9a\u7406<\/strong>\u4ee5\u53ca\u5982\u4f55\u7528\u5b83\u8ba1\u7b97\u77e9\u9635\u7684\u79e9\u3002\u60a8\u8fd8\u5c06\u627e\u5230\u4f7f\u7528\u9c81\u4ec0-\u5f17\u7f57\u8d1d\u5c3c\u4e4c\u65af\u5b9a\u7406\u9010\u6b65\u89e3\u51b3\u7684\u793a\u4f8b\u548c\u7ec3\u4e60\u3002<\/p>\n<h2 class=\"wp-block-heading\">\u4ec0\u4e48\u662f\u9c81\u4ec0-\u5f17\u7f57\u8d1d\u5c3c\u4e4c\u65af\u5b9a\u7406\uff1f<\/h2>\n<p><strong>\u9c81\u4ec0-\u5f17\u7f57\u8d1d\u5c3c\u4e4c\u65af\u5b9a\u7406\u662f\u4e00\u79cd\u5bf9\u7ebf\u6027\u65b9\u7a0b\u7ec4\u8fdb\u884c\u5206\u7c7b\u7684\u65b9\u6cd5\u3002<\/strong>\u6362\u53e5\u8bdd\u8bf4\uff0c\u9c81\u4ec0-\u5f17\u7f57\u8d1d\u5c3c\u4e4c\u65af\u5b9a\u7406\u7528\u4e8e\u627e\u51fa\u65b9\u7a0b\u7ec4\u6709\u591a\u5c11\u4e2a\u89e3\uff0c\u800c\u65e0\u9700\u6c42\u89e3\u5b83\u3002<\/p>\n<p>\u65b9\u7a0b\u7ec4\u6709 3 \u79cd\u7c7b\u578b\uff1a<\/p>\n<ul>\n<li><strong>\u7cfb\u7edf\u517c\u5bb9\u786e\u5b9a\uff08SCD\uff09\uff1a<\/strong>\u7cfb\u7edf\u5177\u6709\u72ec\u7279\u7684\u89e3\u51b3\u65b9\u6848\u3002<\/li>\n<li><strong>\u4e0d\u786e\u5b9a\u517c\u5bb9\u7cfb\u7edf\uff08ICS\uff09\uff1a<\/strong>\u7cfb\u7edf\u6709\u65e0\u9650\u4e2a\u89e3\u3002<\/li>\n<li><strong>\u7cfb\u7edf\u4e0d\u517c\u5bb9\uff08SI\uff09\uff1a<\/strong>\u7cfb\u7edf\u65e0\u89e3\u51b3\u65b9\u6848\u3002<\/li>\n<\/ul>\n<p>\u6b64\u5916\uff0c\u9c81\u4ec0-\u5f17\u7f57\u8d1d\u5c3c\u4e4c\u65af\u5b9a\u7406\u7a0d\u540e\u4e5f\u5c06\u5141\u8bb8\u6211\u4eec<a href=\"https:\/\/mathority.org\/cn\/cramer-\u7684\u89c4\u5219\u793a\u4f8b\u548c\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\/\">\u4f7f\u7528\u514b\u83b1\u9ed8\u89c4\u5219\u6765\u6c42\u89e3\u7cfb\u7edf<\/a>\u3002<\/p>\n<h2 class=\"wp-block-heading\">\u9c81\u4ec0-\u5f17\u7f57\u8d1d\u5c3c\u4e4c\u65af\u5b9a\u7406\u7684\u9648\u8ff0<\/h2>\n<p>\u9c81\u4ec0-\u5f17\u7f57\u8d1d\u5c3c\u4e4c\u65af\u5b9a\u7406\u6307\u51fa<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bd767a13412c19de65e75a6826caee08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{A}\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u662f\u7531\u65b9\u7a0b\u7ec4\u7684\u672a\u77e5\u6570\u7684\u7cfb\u6570\u5f62\u6210\u7684\u77e9\u9635\u3002\u548c\u809a\u5b50<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bf22ad0d457d763be692e97f3bcdf221_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{A'}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u6216<strong>\u6269\u5c55\u77e9\u9635<\/strong>\u662f\u7531\u65b9\u7a0b\u7ec4\u7684\u672a\u77e5\u6570\u548c\u72ec\u7acb\u9879\u7684\u7cfb\u6570\u5f62\u6210\u7684\u77e9\u9635\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><\/figure>\n<\/div>\n<div style=\"background-color:#dff6ff;padding-top: 20px; padding-bottom: 0.5px; padding-right: 40px; padding-left: 30px\" class=\"has-background\">\n<p align=\"LEFT\" style=\"margin-bottom:20px\"><strong>\u9c81\u4ec0-\u5f17\u7f57\u8d1d\u5c3c\u4e4c\u65af\u5b9a\u7406<\/strong>\u8ba9\u6211\u4eec\u80fd\u591f\u6839\u636e\u77e9\u9635 A \u548c A&#8217; \u7684\u79e9\u77e5\u9053\u6211\u4eec\u6b63\u5728\u5904\u7406\u4ec0\u4e48\u7c7b\u578b\u7684\u65b9\u7a0b\u7ec4\uff1a<\/p>\n<ul style=\"color:#E53935; font-weight: bold;\">\n<li style=\"margin-bottom:20px\"><span style=\"color:#000000;font-weight: normal;\">\u5982\u679crank(A)=rank(A&#8217;)=\u672a\u77e5\u6570\u27f6\u786e\u5b9a\u7684\u517c\u5bb9\u7cfb\u7edf(SCD)<\/span><\/li>\n<li style=\"margin-bottom:20px;\"><span style=\"color:#000000;font-weight: normal;\">\u5982\u679crank(A)=rank(A&#8217;)&lt;\u672a\u77e5\u6570\u27f6\u4e0d\u786e\u5b9a\u517c\u5bb9\u7cfb\u7edf(SCI)<\/span><\/li>\n<li><span style=\"color:#000000;font-weight: normal;\">\u5982\u679c\u8303\u56f4(A)\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-be0e48d5500c7e73c450241ea2197789_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{\\neq}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"13\" style=\"vertical-align: -4px;\"><\/p>\n<p><\/span>\u8303\u56f4 (A&#8217;) \u27f6 \u4e0d\u517c\u5bb9\u7cfb\u7edf (SI)<\/li>\n<\/ul>\n<\/div>\n<p>\u4e00\u65e6\u6211\u4eec\u77e5\u9053\u4e86\u9c81\u4ec0-\u5f17\u7f57\u8d1d\u5c3c\u4e4c\u65af\u5b9a\u7406\u7684\u5185\u5bb9\uff0c\u6211\u4eec\u5c31\u4f1a\u770b\u5230\u5982\u4f55\u89e3\u51b3\u9c81\u4ec0-\u5f17\u7f57\u8d1d\u5c3c\u4e4c\u65af\u5b9a\u7406\u7684\u7ec3\u4e60\u3002\u8fd9\u91cc\u6709 3 \u4e2a\u4f8b\u5b50\uff1a\u4f7f\u7528\u6bcf\u79cd\u65b9\u7a0b\u7ec4\u7684\u5b9a\u7406\u6c42\u89e3\u7684\u7ec3\u4e60\u3002<\/p>\n<h2 class=\"wp-block-heading\">\u786e\u5b9a\u7684\u517c\u5bb9\u7cfb\u7edf\u793a\u4f8b\uff08SCD\uff09<\/h2>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b6b2f93c6308c25e8df2fbb5da2af9a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases} 2x+y-3z=0 \\\\[1.5ex] x+2y-z= 1 \\\\[1.5ex] 4x-2y+z = 3\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"135\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u7cfb\u7edf\u7684<strong>\u77e9\u9635A<\/strong>\u548c<strong>\u6269\u5c55\u77e9\u9635A&#8217;<\/strong>\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-4597f5171b586bbcf0915d8512f7b89d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A= \\left( \\begin{array}{ccc} 2 &amp; 1 &amp; -3  \\\\[1.1ex] 1 &amp; 2 &amp; -1  \\\\[1.1ex] 4 &amp; -2 &amp; 1  \\end{array} \\right) \\qquad A'= \\left( \\begin{array}{ccc|c} 2 &amp; 1 &amp; -3 &amp; 0 \\\\[1.1ex] 1 &amp; 2 &amp; -1 &amp; 1  \\\\[1.1ex] 4 &amp; -2 &amp; 1 &amp; 3\\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\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-6c95b7158a2e6401cd16aeb708f128ff_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] 1 &amp; 2 &amp; -1  \\\\[1.1ex] 4 &amp; -2 &amp; 1  \\end{vmatrix} = 25 \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"219\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u7531\u4e8e\u77e9\u9635\u5177\u6709\u4e0d\u540c\u4e8e 0 \u7684 3\u00d73 \u884c\u5217\u5f0f\uff0c<strong>\u56e0\u6b64\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>\u4e00\u65e6\u6211\u4eec\u77e5\u9053\u4e86 A \u7684\u9636\u6570\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u8ba1\u7b97 A&#8217; \u7684\u9636\u6570\uff0c\u5b83\u81f3\u5c11\u662f 3 \u9636\uff0c\u56e0\u4e3a\u6211\u4eec\u521a\u521a\u770b\u5230\u5b83\u5185\u90e8\u6709\u4e00\u4e2a\u4e0d\u540c\u4e8e 0 \u7684 3 \u9636\u884c\u5217\u5f0f\u3002\u800c\u4e14\uff0c\u5b83\u4e0d\u53ef\u80fd\u662f 4 \u9636\uff0c\u56e0\u4e3a\u6211\u4eec\u65e0\u6cd5\u505a\u51fa\u4efb\u4f55 4 \u9636\u884c\u5217\u5f0f\u3002\u56e0\u6b64\uff0c<strong>\u77e9\u9635 A&#8217; \u7684\u79e9\u4e5f\u662f 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-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\u7531\u4e8e\u77e9\u9635 A \u7684\u79e9\u7b49\u4e8e\u77e9\u9635 A&#8217; \u7684\u79e9\u548c\u7cfb\u7edf\u7684\u672a\u77e5\u6570 (3)\uff0c\u56e0\u6b64\u6839\u636e Rouch\u00e9 Frobenius \u5b9a\u7406\uff0c\u6211\u4eec\u77e5\u9053\u5b83\u662f\u4e00\u4e2a<strong>\u517c\u5bb9\u786e\u5b9a\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<h2 class=\"wp-block-heading\">\u4e0d\u786e\u5b9a\u517c\u5bb9\u7cfb\u7edf (ICS) \u793a\u4f8b<\/h2>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2360b9a47257f73cf3f5dea63fb24098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases} x-y+2z=1 \\\\[1.5ex] 3x+2y+z= 5 \\\\[1.5ex] 2x+3y-z = 4\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"135\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u7cfb\u7edf\u7684<strong>\u77e9\u9635A<\/strong>\u548c<strong>\u6269\u5c55\u77e9\u9635A&#8217;<\/strong>\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-b281235e2702433b447e2586ae3092c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A= \\left( \\begin{array}{ccc} 1 &amp; -1 &amp; 2  \\\\[1.1ex] 3 &amp; 2 &amp; 1  \\\\[1.1ex] 2 &amp; 3 &amp; -1  \\end{array} \\right) \\qquad A'= \\left( \\begin{array}{ccc|c} 1 &amp; -1 &amp; 2 &amp; 1 \\\\[1.1ex] 3 &amp; 2 &amp; 1 &amp; 5  \\\\[1.1ex] 2 &amp; 3 &amp; -1 &amp; 4 \\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\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-74cafc27ab41134696c3bf263132b98b_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] 3 &amp; 2 &amp; 1  \\\\[1.1ex] 2 &amp; 3 &amp; -1 \\end{vmatrix} = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"178\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6574\u4e2a\u77e9\u9635A\u7684\u884c\u5217\u5f0f\u4e3a0\uff0c\u6240\u4ee5\u5b83\u4e0d\u662f3\u9636\u7684\u3002\u8981\u5224\u65ad\u5b83\u662f\u5426\u662f2\u9636\u7684\uff0c\u6211\u4eec\u5fc5\u987b\u5728A\u4e2d\u627e\u5230\u4e00\u4e2a\u884c\u5217\u5f0f\u4e0d\u4e3a0\u7684\u5b50\u77e9\u9635\u3002\u4f8b\u5982\uff0c\u4ece\u5de6\u4e0a\u89d2\u5f00\u59cb\u7684\u5b50\u77e9\u9635:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-22b2487f7664a70c116593120de2743b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} 1 &amp; -1  \\\\[1.1ex] 3 &amp; 2 \\end{vmatrix} = 5 \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"123\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\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>\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-17f264ad3859da88ffa6784be24e4143_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix}1 &amp; -1 &amp;  1 \\\\[1.1ex] 3 &amp; 2 &amp; 5  \\\\[1.1ex] 2 &amp; 3 &amp; 4\\end{vmatrix} = 0 \\quad \\begin{vmatrix}1 &amp; 2 &amp; 1 \\\\[1.1ex] 3 &amp;  1 &amp; 5  \\\\[1.1ex] 2 &amp; -1 &amp; 4\\end{vmatrix} = 0 \\quad \\begin{vmatrix} -1 &amp; 2 &amp; 1 \\\\[1.1ex] 2 &amp; 1 &amp; 5  \\\\[1.1ex] 3 &amp; -1 &amp; 4\\end{vmatrix} = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"404\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\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-22b2487f7664a70c116593120de2743b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} 1 &amp; -1  \\\\[1.1ex] 3 &amp; 2 \\end{vmatrix} = 5 \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"123\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64<strong>\u77e9\u9635 A&#8217; \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-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>\u77e9\u9635 A \u7684\u8303\u56f4\u7b49\u4e8e\u77e9\u9635 A&#8217; \u7684\u8303\u56f4\uff0c\u4f46\u5c0f\u4e8e\u7cfb\u7edf\u7684\u672a\u77e5\u6570 (3)\u3002\u56e0\u6b64\uff0c\u6839\u636eRouch\u00e9-Frobenius\u5b9a\u7406\uff0c\u5b83\u662f\u4e00\u4e2a<strong>\u4e0d\u5b9a\u517c\u5bb9\u7cfb\u7edf<\/strong>\uff08ICS\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<h2 class=\"wp-block-heading\">\u4e0d\u517c\u5bb9\u7cfb\u7edf (IS) \u793a\u4f8b<\/h2>\n<div class=\"adsb30\" style=\" margin:px; text-align:\"><\/div>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-30e1084dd637eb4371f6b2218af24136_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases} 2x+y-2z=3 \\\\[1.5ex] 3x-2y+z= 2 \\\\[1.5ex] x+4-5z = 3 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"135\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u7cfb\u7edf\u7684<strong>\u77e9\u9635A<\/strong>\u548c<strong>\u6269\u5c55\u77e9\u9635A&#8217;<\/strong>\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-b435d86f1466af5748d91e6c9bd813e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A= \\left( \\begin{array}{ccc} 2 &amp; 1 &amp; -2 \\\\[1.1ex] 3 &amp; -2 &amp; 1 \\\\[1.1ex] 1 &amp; 4 &amp; -5 \\end{array} \\right) \\qquad A'= \\left( \\begin{array}{ccc|c} 2 &amp; 1 &amp; -2 &amp; 3 \\\\[1.1ex] 3 &amp; -2 &amp; 1 &amp; 2  \\\\[1.1ex] 1 &amp; 4 &amp; -5 &amp; 3 \\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\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-714538c91aa2620a6adb40581245f0e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix}A \\end{vmatrix}= \\begin{vmatrix} 2 &amp; 1 &amp; -2 \\\\[1.1ex] 3 &amp; -2 &amp; 1 \\\\[1.1ex] 1 &amp; 4 &amp; -5 \\end{vmatrix} = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"178\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6574\u4e2a\u77e9\u9635A\u7684\u884c\u5217\u5f0f\u4e3a0\uff0c\u6240\u4ee5\u5b83\u4e0d\u662f3\u9636\u7684\u3002\u8981\u5224\u65ad\u5b83\u662f\u5426\u662f2\u9636\u7684\uff0c\u6211\u4eec\u5fc5\u987b\u5728A\u4e2d\u627e\u5230\u4e00\u4e2a\u884c\u5217\u5f0f\u4e0d\u4e3a0\u7684\u5b50\u77e9\u9635\u3002\u4f8b\u5982\uff0c\u4ece\u5de6\u4e0a\u89d2\u5f00\u59cb\u7684\u5b50\u77e9\u9635:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5a46decda8fd850d9c847922b0c896db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} 2 &amp; 1  \\\\[1.1ex] 3 &amp; -2 \\end{vmatrix} = -7 \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"136\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u7531\u4e8e\u8be5\u77e9\u9635\u5177\u6709\u4e0d\u540c\u4e8e 0 \u7684 2 \u9636\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>\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-47aecdf801b92f21f2287fb96eaaa3f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} 1 &amp; -2 &amp; 3 \\\\[1.1ex]  -2 &amp; 1 &amp; 2  \\\\[1.1ex]  4 &amp; -5 &amp; 3 \\end{vmatrix} = 3 \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"161\" 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\u7531\u4e8e\u77e9\u9635 A \u7684\u79e9\u5c0f\u4e8e\u77e9\u9635 A&#8217; \u7684\u79e9\uff0c\u6211\u4eec\u4ece Rouch\u00e9-Frobenius \u5b9a\u7406\u63a8\u65ad\u5b83\u662f\u4e00\u4e2a<strong>\u4e0d\u76f8\u5bb9\u7cfb\u7edf<\/strong>(SI) <strong>\uff1a<\/strong> <\/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-c3da0513f318d25473e93ba88c51fb42_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<h2 class=\"wp-block-heading\">\u89e3\u51b3\u4e86\u9c81\u4ec0-\u5f17\u7f57\u8d1d\u5c3c\u4e4c\u65af\u5b9a\u7406\u7684\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=\"estil_titol_H3 wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u4f7f\u7528 Rouch\u00e9-Frobenius \u5b9a\u7406\u786e\u5b9a\u4ee5\u4e0b\u5177\u6709 3 \u4e2a\u672a\u77e5\u6570\u7684\u65b9\u7a0b\u7ec4\u7684\u7c7b\u578b\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-theoreme-de-rouche-8211-frebenius-1.webp\" alt=\"\u9c81\u4ec0\u5b9a\u7406\u7684\u6c42\u89e3\u7ec3\u4e60 - \u5f17\u7f57\u8d1d\u5c3c\u4e4c\u65af\" class=\"wp-image-3984\" width=\"193\" 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\">\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-951ce5c1f0c606d4f060a1de58b60303_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; -1 &amp; -1 \\\\[1.1ex] -2 &amp; 4 &amp; 2 \\end{array} \\right) \\qquad A'= \\left( \\begin{array}{ccc|c} 2 &amp; 1 &amp; -3 &amp; 0 \\\\[1.1ex] 3 &amp; -1 &amp; -1 &amp; 2 \\\\[1.1ex] -2 &amp; 4 &amp; 2 &amp; 8 \\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\">\u6211\u4eec\u73b0\u5728\u5fc5\u987b\u627e\u5230\u77e9\u9635 A \u7684\u79e9\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u68c0\u67e5\u77e9\u9635\u7684\u884c\u5217\u5f0f\u662f\u5426\u4e0d\u540c\u4e8e 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-15cddb69f7590648d1d6ae61d942471e_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; -1 &amp; -1 \\\\[1.1ex] -2 &amp; 4 &amp; 2 \\end{vmatrix} = -4+2-36+6+8-6=-30 \\bm{\\neq 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"450\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5177\u6709\u4e0d\u540c\u4e8e 0 \u7684\u4e09\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\">\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 3 \u9636\u7684\uff0c\u56e0\u4e3a\u6211\u4eec\u521a\u521a\u770b\u5230\u5b83\u5185\u90e8\u6709\u4e00\u4e2a\u4e0d\u540c\u4e8e 0 \u7684 3 \u9636\u884c\u5217\u5f0f\u3002\u6b64\u5916\uff0c\u5b83\u4e0d\u80fd\u662f 4 \u9636\u7684\uff0c\u56e0\u4e3a\u6211\u4eec\u4e0d\u80fd\u751f\u6210 4\u00d74 \u7684\u884c\u5217\u5f0f\u3002\u56e0\u6b64\uff0c<strong>\u77e9\u9635 A&#8217; \u7684\u79e9\u4e5f\u662f 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-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\u7531\u4e8e Rouch\u00e9-Frobenius \u5b9a\u7406\uff0c\u6211\u4eec\u77e5\u9053\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<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 Rouch\u00e9-Frobenius \u5b9a\u7406\u5bf9\u4ee5\u4e0b\u5177\u6709 3 \u4e2a\u672a\u77e5\u6570\u7684\u65b9\u7a0b\u7ec4\u8fdb\u884c\u5206\u7c7b\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-theoreme-de-rouche-8211-frebenius-2.webp\" alt=\"Rouche-Frobenius \u5b9a\u7406\u7684\u6c42\u89e3\u7ec3\u4e60\" class=\"wp-image-3987\" width=\"190\" height=\"121\" 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\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-45e13aabe233ece927df7c9ba0bb3ec1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A= \\left( \\begin{array}{ccc}3 &amp; -1 &amp; 2  \\\\[1.1ex] 1 &amp; 2 &amp; -2  \\\\[1.1ex] 1 &amp; -5 &amp; 6 \\end{array} \\right) \\qquad A'= \\left( \\begin{array}{ccc|c} 3 &amp; -1 &amp; 2 &amp; 1 \\\\[1.1ex] 1 &amp; 2 &amp; -2 &amp; 5 \\\\[1.1ex] 1 &amp; -5 &amp; 6 &amp; -9 \\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\u6211\u4eec\u6765\u8ba1\u7b97\u77e9\u9635A\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-87bc95df0033834bba0398b8421faac5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix}A \\end{vmatrix}= \\begin{vmatrix} 3 &amp; -1 &amp; 2 \\\\[1.1ex] 1 &amp; 2 &amp; -2 \\\\[1.1ex] 1 &amp; -5 &amp; 6 \\end{vmatrix} = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"178\" 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-b9805283b75e2b89f67c7865a1263112_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} 3 &amp; -1  \\\\[1.1ex] 1 &amp; 2 \\end{vmatrix} = 7 \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"123\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64<strong>\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\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-e6457fe3f03722b7f0d955191f318915_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix}-1 &amp; 2 &amp; 1 \\\\[1.1ex] 2 &amp; -2 &amp; 5 \\\\[1.1ex] -5 &amp; 6 &amp; -9\\end{vmatrix} = 0 \\quad \\begin{vmatrix}3 &amp; 2 &amp; 1 \\\\[1.1ex] 1 &amp; -2 &amp; 5 \\\\[1.1ex] 1 &amp; 6 &amp; -9\\end{vmatrix} = 0 \\quad \\begin{vmatrix} 3 &amp; -1 &amp; 1 \\\\[1.1ex] 1 &amp; 2 &amp; 5 \\\\[1.1ex] 1 &amp; -5 &amp; -9\\end{vmatrix} = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"446\" 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\u7684\u5185\u90e8\u6709\u8bb8\u591a\u4e0d\u540c\u4e8e0\u76842\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-eafa4747802fae3f0c36350357abbeb2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} -1 &amp; 2  \\\\[1.1ex] 2 &amp; -2 \\end{vmatrix} = -2 \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"150\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64<strong>\u77e9\u9635 A&#8217; \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-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\u8005\u90fd\u5c0f\u4e8e\u7cfb\u7edf\u7684\u672a\u77e5\u6570\u6570 (3)\u3002\u56e0\u6b64\uff0c\u7531Rouch\u00e9-Frobenius\u5b9a\u7406\u6211\u4eec\u77e5\u9053\u5b83\u662f\u4e00\u4e2a<strong>\u4e0d\u5b9a\u76f8\u5bb9\u7cfb\u7edf<\/strong>\uff08ICS\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<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 Rouch\u00e9-Frobenius \u5b9a\u7406\u786e\u5b9a\u4ee5\u4e0b\u65b9\u7a0b\u7ec4\u7684\u7cfb\u7edf\u7c7b\u578b\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-theoreme-de-rouche-8211-frebenius-3.webp\" alt=\"\u7ec3\u4e60\u9010\u6b65\u89e3\u51b3rouche\u5b9a\u7406 - \u5f17\u7f57\u8d1d\u5c3c\u4e4c\u65af\" class=\"wp-image-3990\" width=\"188\" 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\">\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-1820d31e4fd5c79804c9b6fa15abb469_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A= \\left( \\begin{array}{ccc} 1 &amp; 4 &amp; -2 \\\\[1.1ex] 3 &amp; -1 &amp; 3  \\\\[1.1ex] 5 &amp; 7 &amp; -1 \\end{array} \\right) \\qquad A'= \\left( \\begin{array}{ccc|c} 1 &amp; 4 &amp; -2 &amp; 3 \\\\[1.1ex] 3 &amp; -1 &amp; 3 &amp; -2 \\\\[1.1ex] 5 &amp; 7 &amp; -1 &amp; 0 \\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\u6211\u4eec\u6765\u8ba1\u7b97\u77e9\u9635A\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-4f998260ee4c96673085ea6fd4ca87ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix}A \\end{vmatrix}= \\begin{vmatrix} 1 &amp; 4 &amp; -2 \\\\[1.1ex] 3 &amp; -1 &amp; 3 \\\\[1.1ex] 5 &amp; 7 &amp; -1\\end{vmatrix} = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"178\" 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-159a1c58fdcd972b4b08e4795950e064_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} 1 &amp; 4  \\\\[1.1ex] 3 &amp; -1 \\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<strong>\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\u6211\u4eec\u5df2\u7ecf\u77e5\u9053\u524d 3 \u5217\u7684\u884c\u5217\u5f0f\u7ed9\u51fa 0\uff0c\u4f46\u540e 3 \u5217\u7684\u884c\u5217\u5f0f\u5219\u4e0d\u7136\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-c673a5bbbd41933208169fa3e08b7c62_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} 4 &amp; -2 &amp; 3 \\\\[1.1ex]-1 &amp; 3 &amp; -2 \\\\[1.1ex] 7 &amp; -1 &amp; 0 \\end{vmatrix} = -40 \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"198\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c<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 class=\"has-text-align-left\">\u77e9\u9635 A \u7684\u79e9\u5c0f\u4e8e\u77e9\u9635 A&#8217; \u7684\u79e9\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u4ece Rouch\u00e9-Frobenius \u5b9a\u7406\u63a8\u65ad\u51fa\u5b83\u662f\u4e00\u4e2a<strong>\u4e0d\u76f8\u5bb9\u7cfb\u7edf<\/strong>(SI) <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-c3da0513f318d25473e93ba88c51fb42_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<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>\u4f7f\u7528 Rouch\u00e9-Frobenius \u5b9a\u7406\u786e\u5b9a\u4ee5\u4e0b\u5177\u6709 3 \u4e2a\u672a\u77e5\u6570\u7684\u65b9\u7a0b\u7ec4\u7684\u7c7b\u578b\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-theoreme-de-rouche-8211-frobenius-3-inconnues-3-equations.webp\" alt=\"Rouche - Frobenius \u5b9a\u7406\u7528 3 \u4e2a\u672a\u77e5\u6570\u548c 3 \u4e2a\u65b9\u7a0b\u6c42\u89e3\u7ec3\u4e60\" class=\"wp-image-3991\" width=\"203\" 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\">\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-f8a0454c53a64f612c689ba1dae1196b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A= \\left( \\begin{array}{ccc} 5 &amp; -3 &amp; -2  \\\\[1.1ex] 1 &amp; 4 &amp; 1  \\\\[1.1ex]-3 &amp; 2 &amp; -2  \\end{array} \\right) \\qquad A'= \\left( \\begin{array}{ccc|c} 5 &amp; -3 &amp; -2 &amp; -2 \\\\[1.1ex] 1 &amp; 4 &amp; 1 &amp; 7 \\\\[1.1ex]-3 &amp; 2 &amp; -2 &amp; 3 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"446\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u5fc5\u987b\u8ba1\u7b97\u77e9\u9635 A \u7684\u79e9\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u4f7f\u7528 Sarrus \u89c4\u5219\u6c42\u89e3\u77e9\u9635\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-420f0d1ee000f39cbfbce88bf122f413_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix}A \\end{vmatrix}= \\begin{vmatrix} 5 &amp; -3 &amp; -2 \\\\[1.1ex] 1 &amp; 4 &amp; 1 \\\\[1.1ex]-3 &amp; 2 &amp; -2 \\end{vmatrix} = -40+9-4-24-10-6=-75 \\bm{\\neq 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"467\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5177\u6709\u4e0d\u540c\u4e8e 0 \u7684\u4e09\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<strong>\u77e9\u9635 A&#8217; \u7684\u79e9\u4e5f\u662f 3<\/strong> \uff0c\u56e0\u4e3a\u5b83\u59cb\u7ec8\u81f3\u5c11\u662f A \u79e9\uff0c\u5e76\u4e14\u5b83\u4e0d\u80fd\u662f 4 \u79e9\uff0c\u56e0\u4e3a\u6211\u4eec\u65e0\u6cd5\u89e3\u6790\u4efb\u4f55 4\u00d74 \u884c\u5217\u5f0f\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-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\u7531\u4e8e Rouch\u00e9-Frobenius \u5b9a\u7406\u7684\u5e94\u7528\uff0c\u6211\u4eec\u77e5\u9053\u8be5\u7cfb\u7edf\u662f<strong>\u517c\u5bb9\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<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 Rouch\u00e9-Frobenius \u5b9a\u7406\u786e\u5b9a\u4ee5\u4e0b\u65b9\u7a0b\u7ec4\u7684\u7cfb\u7edf\u7c7b\u578b\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-du-theoreme-de-rouche-8211-frebenius.webp\" alt=\"\u9c81\u4ec0\u5b9a\u7406\u7684\u4f8b\u5b50 - \u5f17\u7f57\u8d1d\u5c3c\u4e4c\u65af\" class=\"wp-image-3992\" width=\"205\" 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\">\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-3211e276b2b040969c38bc6c69eabd52_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A= \\left( \\begin{array}{ccc} 4 &amp; -1 &amp; 3 \\\\[1.1ex] -1 &amp; 7 &amp; 3 \\\\[1.1ex] -5 &amp; 8 &amp; 0 \\end{array} \\right) \\qquad A'= \\left( \\begin{array}{ccc|c} 4 &amp; -1 &amp; 3 &amp; 5 \\\\[1.1ex] -1 &amp; 7 &amp; 3 &amp; -3 \\\\[1.1ex] -5 &amp; 8 &amp; 0 &amp; 9 \\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\u6211\u4eec\u6765\u8ba1\u7b97\u77e9\u9635A\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-21004095a3a8ef3edfc15bed5c7853a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix}A \\end{vmatrix}= \\begin{vmatrix} 4 &amp; -1 &amp; 3 \\\\[1.1ex] -1 &amp; 7 &amp; 3 \\\\[1.1ex] -5 &amp; 8 &amp; 0\\end{vmatrix} = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"178\" 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-a58059046b56cf1f8d82c6c8939e44ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} 4 &amp; -1  \\\\[1.1ex]  -1 &amp; 7 \\end{vmatrix} = 27 \\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\"><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\u6211\u4eec\u5df2\u77e5\u7684\u524d 3 \u5217\u7684\u884c\u5217\u5f0f\u7ed9\u51fa 0\uff0c\u4f46\u540e 3 \u5217\u7684\u884c\u5217\u5f0f\u6ca1\u6709\u7ed9\u51fa\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-992718d3b50aedf77c80c262fad5845f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} -1 &amp; 3 &amp; 5 \\\\[1.1ex]  7 &amp; 3 &amp; -3 \\\\[1.1ex] 8 &amp; 0 &amp; 9\\end{vmatrix} = -408 \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"193\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c<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 class=\"has-text-align-left\">\u6700\u540e\uff0c\u6211\u4eec\u5c06\u57df\u5e94\u7528\u5230 Rouch\u00e9-Frobenius \u5b9a\u7406\uff1a\u77e9\u9635 A \u7684\u57df\u5c0f\u4e8e\u77e9\u9635 A&#8217; \u7684\u57df\uff0c\u56e0\u6b64\u5b83\u662f\u4e00\u4e2a<strong>\u4e0d\u76f8\u5bb9\u7cfb\u7edf<\/strong>(SI) <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-c3da0513f318d25473e93ba88c51fb42_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<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e606<\/h3>\n<p>\u4f7f\u7528 Rouch\u00e9-Frobenius \u5b9a\u7406\u5bf9\u4ee5\u4e0b 3 \u9636\u65b9\u7a0b\u7ec4\u8fdb\u884c\u5206\u7c7b\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-d45e8bc425b08e403a98e01693201681_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases} 6x-2y+4z=1 \\\\[1.5ex] -2x+4y+3z= 7 \\\\[1.5ex] 8x-6y+z = -6\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"158\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u6211\u4eec\u9996\u5148\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-8e779eca9135adc44e4a3a55f368560f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A= \\left( \\begin{array}{ccc} 6 &amp; -2 &amp; 4 \\\\[1.1ex] -2 &amp; 4 &amp; 3 \\\\[1.1ex] 8 &amp; -6 &amp; 1  \\end{array} \\right) \\qquad A'= \\left( \\begin{array}{ccc|c} 6 &amp; -2 &amp; 4 &amp; 1 \\\\[1.1ex] -2 &amp; 4 &amp; 3 &amp; 7 \\\\[1.1ex] 8 &amp; -6 &amp; 1 &amp; -6 \\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\u6211\u4eec\u6765\u8ba1\u7b97\u77e9\u9635A\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-c2f63f79858eae462547cf2f270fc780_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix}A \\end{vmatrix}= \\begin{vmatrix} 6 &amp; -2 &amp; 4 \\\\[1.1ex] -2 &amp; 4 &amp; 3 \\\\[1.1ex] 8 &amp; -6 &amp; 1 \\end{vmatrix} = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"178\" 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-e5fa293b94b8c6acfd998f1e154abf7a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} 6 &amp; -2  \\\\[1.1ex] -2 &amp; 4 \\end{vmatrix} = 20  \\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<strong>\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\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-98958f866454a1bf9f1ac078562065cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} -2 &amp; 4 &amp; 1 \\\\[1.1ex]4 &amp; 3 &amp; 7 \\\\[1.1ex] -6 &amp; 1 &amp; -6\\end{vmatrix} = 0 \\quad \\begin{vmatrix}6 &amp; 4 &amp; 1 \\\\[1.1ex] -2 &amp; 3 &amp; 7 \\\\[1.1ex] 8 &amp;  1 &amp; -6\\end{vmatrix} = 0 \\quad \\begin{vmatrix} 6 &amp; -2 &amp; 1 \\\\[1.1ex] -2 &amp; 4 &amp; 7 \\\\[1.1ex] 8 &amp; -6 &amp; -6\\end{vmatrix} = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"446\" 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-58091f1a37a4ef81fdf56f01dd9531a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} 6 &amp; -2 \\\\[1.1ex] -2 &amp; 4 \\end{vmatrix} = 20 \\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<strong>\u77e9\u9635 A&#8217; \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-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\">\u6700\u540e\uff0c\u901a\u8fc7\u5e94\u7528Rouch\u00e9-Frobenius\u5b9a\u7406\uff0c\u6211\u4eec\u77e5\u9053\u5b83\u662f\u4e00\u4e2a<strong>\u4e0d\u5b9a\u76f8\u5bb9\u7cfb\u7edf<\/strong>\uff08ICS\uff09\uff0c\u56e0\u4e3a\u77e9\u9635A\u7684\u8303\u56f4\u7b49\u4e8e\u77e9\u9635A&#8217;\u7684\u8303\u56f4\uff0c\u4f46\u8fd9\u4e24\u8005\u90fd\u5c0f\u4e8e\u77e9\u9635\u4e2d\u672a\u77e5\u6570\u7684\u6570\u91cf\u3002\u7cfb\u7edf(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-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<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u672c\u9875\u4e2d\uff0c\u6211\u4eec\u5c06\u4e86\u89e3\u4ec0\u4e48\u662fRouch\u00e9 Frobenius \u5b9a\u7406\u4ee5\u53ca\u5982\u4f55\u7528\u5b83\u8ba1\u7b97\u77e9\u9635\u7684\u79e9\u3002\u60a8\u8fd8\u5c06\u627e\u5230\u4f7f\u7528\u9c81\u4ec0- &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e5%be%b7%e9%b2%81%e4%bb%80%c2%b7%e5%bc%97%e7%bd%97%e8%b4%9d%e5%b0%bc%e4%b9%8c%e6%96%af%e5%ae%9a%e7%90%86%ef%bc%88%e9%99%84%e7%a4%ba%e4%be%8b%e5%92%8c%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%9a%84%e7%bb%83\/\"> <span class=\"screen-reader-text\">\u9c81\u4ec0-\u5f17\u96f7\u8d1d\u5c3c\u4e4c\u65af\u5b9a\u7406<\/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-297","post","type-post","status-publish","format-standard","hentry","category-18"],"yoast_head":"<!-- This site is optimized 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