{"id":292,"date":"2023-07-06T17:07:12","date_gmt":"2023-07-06T17:07:12","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e7%9f%a9%e9%98%b5%e7%9a%84%e8%8c%83%e5%9b%b4%e4%bd%9c%e4%b8%ba%e5%8f%82%e6%95%b0%e7%9a%84%e5%87%bd%e6%95%b0-%e7%9f%a9%e9%98%b5%e7%9a%84%e7%a4%ba%e4%be%8b%e5%92%8c%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%9a%84\/"},"modified":"2023-07-06T17:07:12","modified_gmt":"2023-07-06T17:07:12","slug":"%e7%9f%a9%e9%98%b5%e7%9a%84%e8%8c%83%e5%9b%b4%e4%bd%9c%e4%b8%ba%e5%8f%82%e6%95%b0%e7%9a%84%e5%87%bd%e6%95%b0-%e7%9f%a9%e9%98%b5%e7%9a%84%e7%a4%ba%e4%be%8b%e5%92%8c%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%9a%84","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e7%9f%a9%e9%98%b5%e7%9a%84%e8%8c%83%e5%9b%b4%e4%bd%9c%e4%b8%ba%e5%8f%82%e6%95%b0%e7%9a%84%e5%87%bd%e6%95%b0-%e7%9f%a9%e9%98%b5%e7%9a%84%e7%a4%ba%e4%be%8b%e5%92%8c%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%9a%84\/","title":{"rendered":"\u57fa\u4e8e\u53c2\u6570\u7684\u6570\u7ec4\u8303\u56f4"},"content":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u4e86\u89e3\u5982\u4f55<strong>\u6839\u636e\u53c2\u6570\u8ba1\u7b97\u8868\u7684\u6392\u540d\u3002<\/strong>\u60a8\u8fd8\u5c06\u627e\u5230\u5173\u4e8e\u5982\u4f55\u6839\u636e\u4e00\u4e2a\u53c2\u6570\u67e5\u627e\u77e9\u9635\u8303\u56f4\u7684\u5206\u6b65\u793a\u4f8b\u548c\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u3002<\/p>\n<p>\u4e3a\u4e86\u5145\u5206\u7406\u89e3\u7814\u7a76\u5e26\u53c2\u6570\u77e9\u9635\u7684\u79e9\u7684\u8fc7\u7a0b\uff0c\u91cd\u8981\u7684\u662f\u60a8\u5df2\u7ecf\u77e5\u9053<a href=\"https:\/\/mathority.org\/cn\">\u5982\u4f55\u901a\u8fc7\u884c\u5217\u5f0f\u8ba1\u7b97\u77e9\u9635\u7684\u79e9<\/a>\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5efa\u8bae\u60a8\u5728\u7ee7\u7eed\u9605\u8bfb\u4e4b\u524d\u5148\u4e86\u89e3\u8fd9\u4e24\u4ef6\u4e8b\u3002<\/p>\n<h2 class=\"wp-block-heading\">\u5982\u4f55\u6839\u636e\u53c2\u6570\u8ba1\u7b97\u6570\u7ec4\u7684\u8303\u56f4\u3002\u4f8b\u5b50\uff1a<\/h2>\n<ul>\n<li>\u6839\u636e\u4e0d\u540c\u7684\u53c2\u6570\u503c\u786e\u5b9a\u77e9\u9635A\u7684\u8303\u56f4\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a48b1eabd1692d9c9da67cbdaef7db3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a :\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"18\" style=\"vertical-align: 0px;\"><\/p>\n<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0aa5688f2845a0225149f448466c943c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A= \\begin{pmatrix} a+1 &amp; -1 &amp; a+1 \\\\[1.1ex] 0 &amp; -1 &amp; 0   \\\\[1.1ex] 1 &amp; -2 &amp; a  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"198\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u77e9\u9635 A \u6700\u591a\u4e3a 3 \u9636\uff0c\u56e0\u4e3a\u5b83\u662f 3 \u9636\u77e9\u9635\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u9996\u5148\u8981\u505a\u7684\u5c31\u662f\u7528<a href=\"https:\/\/mathority.org\/cn\/\u884c\u5217\u5f0f-3x3-sarrus-\u89c4\u5219\u793a\u4f8b\u548c\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\/\">Sarrus \u6cd5\u5219<\/a><strong>\u6c42\u89e3\u6574\u4e2a 3&#215;3 \u77e9\u9635\u7684\u884c\u5217\u5f0f<\/strong>\uff0c\u770b\u80fd\u5426\u8fbe\u5230 3 \u9636\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-835a881061438326519f4660b4c394fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{aligned} \\begin{vmatrix} a+1 &amp; -1 &amp; a+1 \\\\[1.1ex] 0 &amp; -1 &amp; 0   \\\\[1.1ex] 1 &amp; -2 &amp; a  \\end{vmatrix} &amp; =-a(a+1)+0+0+a+1-0-0 \\\\ &amp; =-a^2-a+a+1  \\\\[1.5ex] &amp; =-a^2+1 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"150\" width=\"429\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u884c\u5217\u5f0f\u7684\u7ed3\u679c\u662f\u53c2\u6570\u7684\u51fd\u6570<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1961b1513bd5718956433f1198aa5844_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u3002<strong>\u56e0\u6b64\uff0c\u6211\u4eec\u5c06\u7ed3\u679c\u8bbe\u7f6e\u4e3a 0\uff0c<\/strong>\u4ee5\u67e5\u770b\u8868\u4f55\u65f6\u4e3a 2 \u7ea7\u4ee5\u53ca\u4f55\u65f6\u4e3a 3 \u7ea7\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7cf08fe725290ac099f54916fa4c5dcf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle -a^2+1 = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"93\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u6c42\u89e3\u6240\u5f97\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-18b6f04242243eeefa0cd5892b29f4d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a^2 = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"49\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ad7c0d92bbec913193a85949c7a0bfa2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\sqrt{a^2} = \\sqrt{1}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"78\" style=\"vertical-align: -1px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1191c881d84f673236382966b4e709ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{a = \\pm 1}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"55\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u5f53<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1961b1513bd5718956433f1198aa5844_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u65e0\u8bba\u662f+1\u8fd8\u662f-1\uff0c3\u00d73\u884c\u5217\u5f0f\u90fd\u5c06\u4e3a0\uff0c\u56e0\u6b64\u77e9\u9635\u7684\u79e9\u4e0d\u4f1a\u4e3a3\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5f53<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1961b1513bd5718956433f1198aa5844_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4e0e +1 \u548c -1 \u4e0d\u540c\uff0c\u884c\u5217\u5f0f\u5c06\u4e0d\u540c\u4e8e 0\uff0c\u56e0\u6b64\u77e9\u9635\u7684\u79e9\u4e3a 3\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-60e6f80d73c96b28458d7790d98d0a5a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\color{blue} \\boxed{ \\begin{array}{c}  \\\\[-2ex] \\color{black}\\phantom{33} \\bm{a \\neq +1,-1 \\ \\longrightarrow \\ Rg(A)=3} \\phantom{33} \\\\[-2ex] &amp; \\end{array} }\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"354\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u8ba9\u6211\u4eec\u770b\u770b\u5f53<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bbdf9897658213f9f2ad0b6a3d8d87cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{a=+1} :\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"65\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-53dde6f61dc01cac5c0a0705c44a7433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a = +1 \\longrightarrow A= \\begin{pmatrix} 2 &amp; -1 &amp; 2 \\\\[1.1ex] 0 &amp; -1 &amp; 0   \\\\[1.1ex] 1 &amp; -2 &amp; 1  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"230\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6b63\u5982\u6211\u4eec\u4e4b\u524d\u770b\u5230\u7684\uff0c\u5f53<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1961b1513bd5718956433f1198aa5844_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4e3a 1 \u65f6\uff0c\u77e9\u9635\u7684\u884c\u5217\u5f0f\u4e3a 0\u3002\u56e0\u6b64\u5b83\u7684\u79e9\u4e0d\u80fd\u4e3a 3\u3002\u73b0\u5728\u6211\u4eec\u5c1d\u8bd5\u8ba1\u7b97<a href=\"https:\/\/mathority.org\/cn\/\u884c\u5217\u5f0f-2x2-\u793a\u4f8b\u548c\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\/\">\u77e9\u9635\u5185\u90e8\u4e0e 0 \u4e0d\u540c\u7684 2\u00d72 \u884c\u5217\u5f0f<\/a>\uff0c\u4f8b\u5982\u5de6\u4e0a\u89d2\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-d291f322f9d3f392e46568817e531a84_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle   \\begin{vmatrix} 2 &amp; -1 \\\\[1.1ex] 0 &amp; -1 \\end{vmatrix} =-2-0= -2 \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"213\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> 2 \u9636\u884c\u5217\u5f0f\u4e0d\u7b49\u4e8e 0\u3002\u56e0\u6b64\uff0c\u5f53\u53c2\u6570<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1961b1513bd5718956433f1198aa5844_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u6216 +1\uff0c<strong>\u77e9\u9635\u7684\u79e9\u5c06\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-d00c47041db87183749744eaf6789fd0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\color{blue} \\boxed{ \\begin{array}{c}  \\\\[-2ex] \\color{black} \\phantom{33} \\bm{a = +1 \\ \\longrightarrow \\ Rg(A)=2} \\phantom{33} \\\\[-2ex] &amp; \\end{array} }\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"323\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u4e00\u65e6\u6211\u4eec\u770b\u5230\u77e9\u9635\u7684\u8303\u56f4<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-910ad8735da02f7dffe9cd0fda341d6c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a \\neq +1,-1\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"86\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u4ec0\u4e48\u65f6\u5019<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-10f3012b6955e51b81c57a6e2e57b7df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a=+1\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"55\" style=\"vertical-align: -2px;\"><\/p>\n<p>\u8ba9\u6211\u4eec\u770b\u770b\u5f53<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3d04c75a36ec68cca9920060cc558b99_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{a = -1} :\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" 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-f723d9c6b9f786b8c405ac7ec2d8bf1d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a = -1 \\longrightarrow A=  \\begin{pmatrix} 0 &amp; -1 &amp; 0 \\\\[1.1ex] 0 &amp; -1 &amp; 0   \\\\[1.1ex] 1 &amp; -2 &amp; -1  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"244\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6b63\u5982\u6211\u4eec\u4e00\u5f00\u59cb\u6240\u770b\u5230\u7684\uff0c\u5f53<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1961b1513bd5718956433f1198aa5844_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>es -1 \u5e76\u4e14\u77e9\u9635\u7684\u884c\u5217\u5f0f\u4e3a0\u3002\u56e0\u6b64\uff0c\u4e0d\u80fd\u5c06\u5176\u8bbe\u7f6e\u4e3a\u79e93\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5e94\u8be5\u5c1d\u8bd5\u5728\u77e9\u9635\u4e2d\u9047\u5230\u4e0d\u540c\u4e8e0\u76842\u00d72\u7684\u884c\u5217\u5f0f\uff0c\u4f8b\u5982\u4e0b\u77e9\u9635\u7684\u4e00\u90e8\u5206\u3002\u5de6\u8fb9\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cdc9bd6d9ad083e1e38f53079aebb5e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle   \\begin{vmatrix} 0 &amp; -1 \\\\[1.1ex] 1 &amp; -2  \\end{vmatrix} = 0-(-1)= 1\\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"213\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u7ef4\u5ea6 2 \u7684\u884c\u5217\u5f0f\u4e0d\u540c\u4e8e 0\u3002\u56e0\u6b64\uff0c\u5f53\u53c2\u6570<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1961b1513bd5718956433f1198aa5844_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u6216 -1\uff0c<strong>\u8868\u7684\u7b49\u7ea7\u5c06\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-d12346bae2f327e7e1ee6c5276a599cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\color{blue} \\boxed{ \\begin{array}{c} \\\\[-2ex] \\color{black} \\phantom{33} \\bm{a = -1 \\ \\longrightarrow \\ Rg(A)=2} \\phantom{33} \\\\[-2ex] &amp; \\end{array} }\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"323\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u6211\u4eec\u53d1\u73b0\u4e86 3 \u79cd\u4e0d\u540c\u7684\u60c5\u51b5\uff0c\u5176\u4e2d\u77e9\u9635 A \u7684\u79e9\u53d6\u51b3\u4e8e\u53c2\u6570\u53d6\u7684\u503c<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4ae924c776e55c0f2987a783307cd9fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p><strong>\u603b\u7ed3<\/strong>\u5982\u4e0b\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dc3a7ebea32c871ab7971a276decc60a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\color{blue} \\boxed{ \\begin{array}{c} \\\\ \\color{black} \\phantom{33} \\bm{a \\neq +1,-1 \\ \\longrightarrow \\ Rg(A)=3} \\phantom{33} \\\\[3ex] \\color{black} \\bm{a = +1 \\ \\longrightarrow \\ Rg(A)=2} \\\\[3ex]  \\color{black} \\bm{a = -1 \\ \\longrightarrow \\ Rg(A)=2} \\\\ &amp; \\end{array} }\" title=\"Rendered by QuickLaTeX.com\" height=\"167\" width=\"354\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u60a8\u5df2\u7ecf\u77e5\u9053\u5982\u4f55\u8ba8\u8bba\u53c2\u6570\u76f8\u5173\u77e9\u9635\u7684\u8303\u56f4\uff0c\u60a8\u53ef\u4ee5\u7ec3\u4e60\u4e0b\u9762\u7684\u5206\u6b65\u7ec3\u4e60\u3002\u8981\u89e3\u51b3\u8fd9\u4e9b\u95ee\u9898\uff0c<a href=\"https:\/\/mathority.org\/cn\/\u884c\u5217\u5f0f\u7684\u6027\u8d28-\u793a\u4f8b\u548c\u7ec3\u4e60-2x2-3x3\/\">\u9650\u5b9a\u8bcd\u7684\u5c5e\u6027<\/a>\u80af\u5b9a\u4f1a\u5bf9\u60a8\u6709\u6240\u5e2e\u52a9\uff0c\u56e0\u6b64\uff0c\u5982\u679c\u60a8\u5bf9\u5b83\u4eec\u4e0d\u662f\u5f88\u6e05\u695a\uff0c\u6211\u5efa\u8bae\u60a8\u9996\u5148\u770b\u4e00\u4e0b\u94fe\u63a5\u7684\u9875\u9762\uff0c\u5176\u4e2d\u6bcf\u4e2a\u5c5e\u6027\u90fd\u901a\u8fc7\u793a\u4f8b\u8fdb\u884c\u4e86\u89e3\u91ca\u3002<\/p>\n<h2 class=\"wp-block-heading\">\u4fee\u590d\u4e86\u57fa\u4e8e\u53c2\u6570\u7684\u77e9\u9635\u8303\u56f4\u95ee\u9898<\/h2>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u6839\u636e\u53c2\u6570\u503c\u7814\u7a76\u4e0b\u8868\u8303\u56f4<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a48b1eabd1692d9c9da67cbdaef7db3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a :\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"18\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d7f53b08bcf2e2660dbb7c0aeb6fd369_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\begin{pmatrix} 3 &amp; 1 &amp; a \\\\[1.1ex] 2 &amp; 2 &amp; -4 \\\\[1.1ex] 2 &amp; 1 &amp; 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"136\" 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\">\u77e9\u9635 A \u6700\u591a\u5177\u6709 3 \u9636\uff0c\u56e0\u4e3a\u5b83\u662f\u4e00\u4e2a 3\u00d73 \u77e9\u9635\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u9996\u5148\u8981\u505a\u7684\u662f\u6c42\u89e3\u6574\u4e2a\u77e9\u9635\u7684\u884c\u5217\u5f0f\uff08\u4f7f\u7528\u8428\u9c81\u65af\u89c4\u5219\uff09\uff0c\u770b\u770b\u5b83\u662f\u5426\u53ef\u4ee5\u8fbe\u52303\u9636\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d2539698cbcf9f06d2890d17da76174f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} 3 &amp; 1 &amp; a \\\\[1.1ex] 2 &amp; 2 &amp; -4 \\\\[1.1ex] 2 &amp; 1 &amp; 0 \\end{vmatrix}  =0-8+2a-4a+12-0 =-2a+4\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"382\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u5c06\u7ed3\u679c\u8bbe\u7f6e\u4e3a 0 \u6765\u67e5\u770b\u6570\u7ec4\u4f55\u65f6\u4e3a 2 \u7ea7\u4ee5\u53ca\u4f55\u65f6\u4e3a 3 \u7ea7\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7042ae953fdcbe91d08fa963be26f7c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle -2a+4=0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"94\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-90183d93145fd04e7a774c8a72bc3f1d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle -2a=-4\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"78\" 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-21d4999dede651fdb38c5b047b8e805d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle a=\\cfrac{-4}{-2} = 2\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"97\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u5f53<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1961b1513bd5718956433f1198aa5844_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4e0e 2 \u4e0d\u540c\uff0c\u884c\u5217\u5f0f 3\u00d73 \u5c06\u4e0e 0 \u4e0d\u540c\uff0c\u56e0\u6b64\u77e9\u9635\u7684\u79e9\u5c06\u4e3a 3\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-a4c4e0bfd1194afe82d8807c033e7551_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\color{blue} \\boxed{ \\begin{array}{c} \\\\[-2ex] \\color{black}\\phantom{33} \\bm{a \\neq 2 \\ \\longrightarrow \\ Rg(A)=3} \\phantom{33} \\\\[-2ex] &amp; \\end{array} }\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"310\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u8ba9\u6211\u4eec\u770b\u770b\u5f53<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f2abbabd80372bf9bc248f12cebd5fb9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a=2 :\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"51\" 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-c131e19dd5d5c0d7826306103b4e118b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a = 2 \\longrightarrow A= \\begin{pmatrix} 3 &amp; 1 &amp; 2 \\\\[1.1ex] 2 &amp; 2 &amp; -4 \\\\[1.1ex] 2 &amp; 1 &amp; 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"216\" 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-b97f01989b5e9679f95d300cd64f3735_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] 2 &amp; 2 &amp; -4 \\\\[1.1ex] 2 &amp; 1 &amp; 0 \\end{vmatrix}= 0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"164\" 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-77b38ebf03b8ed059edefd523c5ca1f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} 3 &amp; 1  \\\\[1.1ex] 2 &amp; 2 \\end{vmatrix} = 6-2 = 4 \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"172\" 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-1f174f72890bce94d148e1f6e88681ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\color{blue} \\boxed{ \\begin{array}{c} \\\\[-2ex] \\color{black} \\phantom{33} \\bm{a = 2 \\ \\longrightarrow \\ Rg(A)=2} \\phantom{33} \\\\[-2ex] &amp; \\end{array} }\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"310\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u6211\u4eec\u53d1\u73b0\u4e86\u4e24\u79cd\u60c5\u51b5\uff0c\u5176\u4e2d\u77e9\u9635 A \u7684\u8303\u56f4\u968f\u53c2\u6570\u53d6\u503c\u7684\u53d8\u5316\u800c\u53d8\u5316\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-41e5cc7b6e9b3204f26e1c64e46f7057_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\color{blue} \\boxed{ \\begin{array}{c} \\\\ \\color{black} \\phantom{33} \\bm{a \\neq 2 \\longrightarrow \\ Rg(A)=3} \\phantom{33} \\\\[3ex] \\color{black} \\bm{a = 2\\ \\longrightarrow \\ Rg(A)=2}  \\\\ &amp; \\end{array} }\" title=\"Rendered by QuickLaTeX.com\" height=\"122\" width=\"304\" 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>\u6839\u636e\u53c2\u6570\u503c\u67e5\u627e\u4e0b\u8868\u7684\u8303\u56f4<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a48b1eabd1692d9c9da67cbdaef7db3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a :\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"18\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5b28f21cc2e7211d9dae9b6685b541fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\begin{pmatrix} 2 &amp; 2 &amp; 1 \\\\[1.1ex] a &amp; 1 &amp; 3 \\\\[1.1ex] -2 &amp; -2 &amp; a \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"150\" 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\">\u77e9\u9635 A \u6700\u591a\u5177\u6709 3 \u9636\uff0c\u56e0\u4e3a\u5b83\u662f\u4e00\u4e2a 3\u00d73 \u77e9\u9635\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u9996\u5148\u8981\u505a\u7684\u662f\u6c42\u89e3\u6574\u4e2a\u77e9\u9635\u7684\u884c\u5217\u5f0f\uff08\u4f7f\u7528\u8428\u9c81\u65af\u89c4\u5219\uff09\uff0c\u770b\u770b\u5b83\u662f\u5426\u53ef\u4ee5\u8fbe\u52303\u9636\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-30c8c16fea09001059a5d66727fc7be3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{aligned} \\begin{vmatrix} 2 &amp; 2 &amp; 1 \\\\[1.1ex] a &amp; 1 &amp; 3 \\\\[1.1ex] -2 &amp; -2 &amp; a \\end{vmatrix} &amp; =2a-12-2a+2+12-2a^2 \\\\ &amp;=2-2a^2\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"335\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u5c06\u7ed3\u679c\u8bbe\u7f6e\u4e3a 0 \u6765\u67e5\u770b\u6570\u7ec4\u4f55\u65f6\u4e3a 2 \u7ea7\u4ee5\u53ca\u4f55\u65f6\u4e3a 3 \u7ea7\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-28c4eeb004bd0bf3db692ee22c659a40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 2-2a^2=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"89\" 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-e39820ff30d5df06ac09f254dcebeef0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle -2a^2=-2\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"84\" 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-3c5cad133a274f40a2151ad9e9310825_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle a^2=\\cfrac{-2}{-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"74\" 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-8b5cd6314cc67aa83d49e16072e9314b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle a^2=1\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"49\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-63f049dc27947cfc24afdd331acefe23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle a=\\pm 1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"55\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u5f53<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1961b1513bd5718956433f1198aa5844_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4e0e +1 \u548c -1 \u4e0d\u540c\uff0c3\u00d73 \u884c\u5217\u5f0f\u5c06\u4e0d\u540c\u4e8e 0\uff0c\u56e0\u6b64\u77e9\u9635\u7684\u79e9\u5c06\u4e3a 3\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-e7d26d825cd80ee861dd13168dafd408_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\color{blue} \\boxed{ \\begin{array}{c} \\\\[-2ex] \\color{black}\\phantom{33} \\bm{a \\neq +1, -1 \\ \\longrightarrow \\ Rg(A)=3} \\phantom{33} \\\\[-2ex] &amp; \\end{array} }\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"354\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u8ba9\u6211\u4eec\u770b\u770b\u5f53<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ee9005a2708f5bcb0f0fba0cefed3dfe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a=+1 :\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"65\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7b95d408f076c4978c8605380a277cdf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a = +1 \\longrightarrow A= \\begin{pmatrix} 2 &amp; 2 &amp; 1 \\\\[1.1ex] 1 &amp; 1 &amp; 3 \\\\[1.1ex] -2 &amp; -2 &amp; 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"244\" 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-fcd50b9549925b5011a6c20943c326ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} A \\end{vmatrix} = \\begin{vmatrix} 2 &amp; 2 &amp; 1 \\\\[1.1ex] 1 &amp; 1 &amp; 3 \\\\[1.1ex] -2 &amp; -2 &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-03242296f208e07b9c4d634f0b7724cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix}  2 &amp; 1 \\\\[1.1ex]  1 &amp; 3 \\end{vmatrix} = 6-1 = 5 \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"172\" 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-2550b439990981d1b74f72b1649a57e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\color{blue} \\boxed{ \\begin{array}{c} \\\\[-2ex] \\color{black} \\phantom{33} \\bm{a = +1 \\ \\longrightarrow \\ Rg(A)=2} \\phantom{33} \\\\[-2ex] &amp; \\end{array} }\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"323\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u8ba9\u6211\u4eec\u770b\u770b\u5f53<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-53cc36b0e502c4e9a0aa575015035a8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a=-1 :\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" 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-a2d16421400df26760d811229215ac83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a = -1 \\longrightarrow A= \\begin{pmatrix} 2 &amp; 2 &amp; 1 \\\\[1.1ex] -1 &amp; 1 &amp; 3 \\\\[1.1ex] -2 &amp; -2 &amp; -1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"258\" 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-ecd0b86cd6c59a0911f0c39ca7599806_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} A \\end{vmatrix} = \\begin{vmatrix} 2 &amp; 2 &amp; 1 \\\\[1.1ex] -1 &amp; 1 &amp; 3 \\\\[1.1ex] -2 &amp; -2 &amp; -1  \\end{vmatrix}= 0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"191\" 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-378e43f0ef61ccabf82dacb5ac70466f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} 2 &amp; 2  \\\\[1.1ex] -1 &amp; 1 \\end{vmatrix} =2-(-2) = 4 \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"213\" 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-d12346bae2f327e7e1ee6c5276a599cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\color{blue} \\boxed{ \\begin{array}{c} \\\\[-2ex] \\color{black} \\phantom{33} \\bm{a = -1 \\ \\longrightarrow \\ Rg(A)=2} \\phantom{33} \\\\[-2ex] &amp; \\end{array} }\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"323\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u6211\u4eec\u53d1\u73b0\u4e86 3 \u79cd\u60c5\u51b5\uff0c\u5176\u4e2d\u77e9\u9635 A \u7684\u8303\u56f4\u6839\u636e\u53c2\u6570\u53d6\u503c\u800c\u53d8\u5316\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6bf1904cee51914e041d94f588fed84d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\color{blue} \\boxed{ \\begin{array}{c} \\\\ \\color{black} \\phantom{33} \\bm{a \\neq +1,-1 \\longrightarrow \\ Rg(A)=3} \\phantom{33} \\\\[3ex] \\color{black} \\bm{a = +1\\ \\longrightarrow \\ Rg(A)=2} \\\\[3ex] \\color{black} \\bm{a = -1\\ \\longrightarrow \\ Rg(A)=2}  \\\\ &amp; \\end{array} }\" title=\"Rendered by QuickLaTeX.com\" height=\"167\" width=\"348\" 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:px; text-align:\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e603<\/h3>\n<p>\u6839\u636e\u53c2\u6570\u503c\u8ba1\u7b97\u4e0b\u8868\u7684\u8303\u56f4<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a48b1eabd1692d9c9da67cbdaef7db3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a :\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"18\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-090a99d3b4111785433e5c769589eb01_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\begin{pmatrix} a+1 &amp; 1 &amp; -5 \\\\[1.1ex] 0 &amp; 1 &amp; -2 \\\\[1.1ex] -1 &amp; 3 &amp; a-3  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"184\" 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\">\u77e9\u9635 A \u6700\u591a\u5177\u6709 3 \u9636\uff0c\u56e0\u4e3a\u5b83\u662f\u4e00\u4e2a 3\u00d73 \u77e9\u9635\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u9996\u5148\u8981\u505a\u7684\u662f\u6c42\u89e3\u6574\u4e2a\u77e9\u9635\u7684\u884c\u5217\u5f0f\uff08\u4f7f\u7528\u8428\u9c81\u65af\u89c4\u5219\uff09\uff0c\u770b\u770b\u5b83\u662f\u5426\u53ef\u4ee5\u8fbe\u52303\u9636\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fec1cb52bb87fa2bccb40b70e1f21c7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{aligned} \\begin{vmatrix} a+1 &amp; 1 &amp; -5 \\\\[1.1ex] 0 &amp; 1 &amp; -2 \\\\[1.1ex] -1 &amp; 3 &amp; a-3 \\end{vmatrix} &amp; =(a+1)(a-3) +2+0-5+6(a+1)-0 \\\\ &amp; = a^2-3a+a-3 +2-5+6a+6 \\\\[1.5ex] &amp; =a^2+4a\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"150\" width=\"468\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u5c06\u7ed3\u679c\u8bbe\u7f6e\u4e3a 0 \u6765\u67e5\u770b\u6570\u7ec4\u4f55\u65f6\u4e3a 2 \u7ea7\u4ee5\u53ca\u4f55\u65f6\u4e3a 3 \u7ea7\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f8e26b9f10414656086a0c25d28ea04f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle a^2+4a=0\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"90\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8fd9\u662f\u4e00\u4e2a\u4e0d\u5b8c\u5168\u4e8c\u6b21\u65b9\u7a0b\uff0c\u6240\u4ee5\u6211\u4eec\u63d0\u53d6\u4e00\u4e2a\u516c\u56e0\u5b50\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3f6035239798b59504a776dac1f0e21a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle a(a+4)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"96\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u5c06\u6bcf\u4e00\u9879\u8bbe\u7f6e\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-43b38da320da538e46c6b4515de48568_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a(a+4)=0 \\longrightarrow \\begin{cases} \\bm{a = 0} \\\\[2ex] a+4=0  \\ \\longrightarrow \\ \\bm{a=-4}\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"328\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u5f97\u5230 0 \u548c -4 \u4f5c\u4e3a\u89e3\u3002\u56e0\u6b64\uff0c\u5f53<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1961b1513bd5718956433f1198aa5844_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4e0d\u540c\u4e8e 0 \u548c -4\uff0c3\u00d73 \u884c\u5217\u5f0f\u5c06\u4e0d\u540c\u4e8e 0\uff0c\u56e0\u6b64\u77e9\u9635\u7684\u79e9\u5c06\u4e3a 3\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-15908960ef2cfcd2105c4b901fb6cb49_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\color{blue} \\boxed{ \\begin{array}{c} \\\\[-2ex] \\color{black}\\phantom{33} \\bm{a \\neq 0, -4 \\ \\longrightarrow \\ Rg(A)=3} \\phantom{33} \\\\[-2ex] &amp; \\end{array} }\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"340\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u8ba9\u6211\u4eec\u770b\u770b\u5f53<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d229e6228a70e103acbec8ca88c12d7a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a=0 :\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"51\" 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-d97b25f01cb00d4677da0de5b4340ddb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a = 0 \\longrightarrow A= \\begin{pmatrix} 1 &amp; 1 &amp; -5 \\\\[1.1ex] 0 &amp; 1 &amp; -2 \\\\[1.1ex] -1 &amp; 3 &amp; -3 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"230\" 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-9e0f3c315588dff8274873001f727a69_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} A \\end{vmatrix} = \\begin{vmatrix} 1 &amp; 1 &amp; -5 \\\\[1.1ex] 0 &amp; 1 &amp; -2 \\\\[1.1ex] -1 &amp; 3 &amp; -3 \\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-c132b22650c707d9f410c3d9c1e8da35_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} 1 &amp; 1  \\\\[1.1ex] 0 &amp; 1 \\end{vmatrix} = 1-0 = 1 \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"172\" 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-d33aeec452b54112a958bfeadf014fe2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\color{blue} \\boxed{ \\begin{array}{c} \\\\[-2ex] \\color{black} \\phantom{33} \\bm{a = 0 \\ \\longrightarrow \\ Rg(A)=2} \\phantom{33} \\\\[-2ex] &amp; \\end{array} }\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"310\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u8ba9\u6211\u4eec\u770b\u770b\u5f53<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0287c5c8b769f316fb7d382ea3332fa7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a=-4 :\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" 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-9ce7e40d9d78ecddc5ee81fc799c8767_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a = -4 \\longrightarrow A= \\begin{pmatrix} -3 &amp; 1 &amp; -5 \\\\[1.1ex] 0 &amp; 1 &amp; -2 \\\\[1.1ex] -1 &amp; 3 &amp; -7  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"244\" 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-52d15d0bceeb1dbbc415fb4825ce9a05_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} A \\end{vmatrix} = \\begin{vmatrix} -3 &amp; 1 &amp; -5 \\\\[1.1ex] 0 &amp; 1 &amp; -2 \\\\[1.1ex] -1 &amp; 3 &amp; -7 \\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-d45971f1dbda32405246de38bb68bd92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} -3 &amp; 1 \\\\[1.1ex] 0 &amp; 1\\end{vmatrix} =-3-0 = -3 \\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"213\" 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-0551d4c8535193e378fc38c2e5580157_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\color{blue} \\boxed{ \\begin{array}{c} \\\\[-2ex] \\color{black} \\phantom{33} \\bm{a = -4 \\ \\longrightarrow \\ Rg(A)=2} \\phantom{33} \\\\[-2ex] &amp; \\end{array} }\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"323\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u6211\u4eec\u53d1\u73b0\u4e86 3 \u79cd\u60c5\u51b5\uff0c\u5176\u4e2d\u77e9\u9635 A \u7684\u8303\u56f4\u6839\u636e\u53c2\u6570\u53d6\u503c\u800c\u53d8\u5316\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-844f152985a2d84be1456501dfdc16e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\color{blue} \\boxed{ \\begin{array}{c} \\\\ \\color{black} \\phantom{33} \\bm{a \\neq 0,-4 \\longrightarrow \\ Rg(A)=3} \\phantom{33} \\\\[3ex] \\color{black} \\bm{a = 0\\ \\longrightarrow \\ Rg(A)=2} \\\\[3ex] \\color{black} \\bm{a = -4\\ \\longrightarrow \\ Rg(A)=2}  \\\\ &amp; \\end{array} }\" title=\"Rendered by QuickLaTeX.com\" height=\"167\" width=\"334\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e604<\/h3>\n<p>\u6839\u636e\u53c2\u6570\u7684\u503c\u6c42\u4ee5\u4e0b3\u00d74\u7ef4\u77e9\u9635\u7684\u8303\u56f4<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a48b1eabd1692d9c9da67cbdaef7db3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a :\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"18\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4da7907bd0e8f80006ea47d2437b3f3d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\begin{pmatrix} -1&amp;-3&amp;-2&amp;1\\\\[1.1ex] 4&amp;12&amp;8&amp;-4\\\\[1.1ex] 2&amp;6&amp;4&amp;a \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"203\" 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\">\u77e9\u9635 A \u6700\u591a\u4e3a 3 \u9636\uff0c\u56e0\u4e3a\u6211\u4eec\u65e0\u6cd5\u8ba1\u7b97\u4efb\u4f55<a href=\"https:\/\/mathority.org\/cn\/4x4-\u884c\u5217\u5f0f\u7684\u8865\u5145\u793a\u4f8b\u548c\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\/\">4\u00d74 \u884c\u5217\u5f0f<\/a>\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u8981\u505a\u7684\u7b2c\u4e00\u4ef6\u4e8b\u662f\u6c42\u89e3\u6240\u6709\u53ef\u80fd\u7684 3 \u9636\u884c\u5217\u5f0f\uff08\u4f7f\u7528 Sarrus \u89c4\u5219\uff09\uff0c\u770b\u770b\u5b83\u662f\u5426\u53ef\u4ee5\u662f 3 \u9636\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c2db025b8ecf4323d4a912d84a215d8e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{aligned} \\begin{vmatrix} -1&amp;-3&amp;-2\\\\[1.1ex] 4&amp;12&amp;8\\\\[1.1ex] 2&amp;6&amp;4 \\end{vmatrix} &amp; =-48-48-48+48+48+48 =\\bm{0}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"395\" 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-e40592bf6f8bfd13cb68a1fd0393cebb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{aligned} \\begin{vmatrix} -1&amp;-3&amp;1\\\\[1.1ex] 4&amp;12&amp;-4\\\\[1.1ex] 2&amp;6&amp;a \\end{vmatrix} &amp; =-12a+24+24-24-24+12a=\\bm{0}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"414\" 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-ce1c28ae4120f0b37059b763e576d2eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{aligned} \\begin{vmatrix} -1&amp;-2&amp;1\\\\[1.1ex] 4&amp;8&amp;-4\\\\[1.1ex] 2&amp;4&amp;a \\end{vmatrix} &amp; =-8a+16+16-16-16+8a=\\bm{0}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"396\" 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-668e9096b00b90ee4cc48d272b17e7bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{aligned} \\begin{vmatrix} -3&amp;-2&amp;1\\\\[1.1ex] 12&amp;8&amp;-4\\\\[1.1ex] 6&amp;4&amp;a \\end{vmatrix} &amp; =-24a+48+48-48-48+24a=\\bm{0}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"414\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u65e0\u8bba 3 \u9636\u884c\u5217\u5f0f\u7684\u503c\u662f\u591a\u5c11\uff0c\u6240\u6709\u53ef\u80fd\u7684\u884c\u5217\u5f0f\u7684\u7ed3\u679c\u90fd\u662f 0<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1961b1513bd5718956433f1198aa5844_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u3002\u56e0\u6b64\u77e9\u9635\u6c38\u8fdc\u4e0d\u4f1a\u662f 3 \u9636\uff0c\u56e0\u4e3a\u5b83\u53d6\u4ec0\u4e48\u503c\u5e76\u4e0d\u91cd\u8981<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1961b1513bd5718956433f1198aa5844_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u9664\u4e86 0 \u4e4b\u5916\uff0c\u6c38\u8fdc\u4e0d\u4f1a\u5b58\u5728 3\u00d73 \u884c\u5217\u5f0f\u3002<\/p>\n<p class=\"has-text-align-left\">\u6240\u4ee5\u73b0\u5728\u6211\u4eec\u5c1d\u8bd5 2 \u00d7 2 \u7ef4\u7684\u884c\u5217\u5f0f\u3002\u4f46\u662f\uff0c\u9664\u4e86\u4ee5\u4e0b\u5404\u9879\u4e4b\u5916\uff0c\u6240\u6709 2 \u9636\u884c\u5217\u5f0f\u4e5f\u90fd\u7ed9\u51fa 0\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c4408f1ccf562196943209356e50e892_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{aligned} \\begin{vmatrix} 8&amp;-4\\\\[1.1ex] 4&amp;a \\end{vmatrix} &amp; =8a+16 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"139\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u5c06\u7ed3\u679c\u8bbe\u7f6e\u4e3a 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-f5494bb524be48bc22a1cb054556c3a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 8a+16=0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"90\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8a6fc020bc84c4ba3f1989065a2207fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 8a=-16\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"74\" 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-02680bced4f2a76a7d23c5b9e6a2ecbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle a=\\cfrac{-16}{8} =-2\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"120\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u5f53<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1961b1513bd5718956433f1198aa5844_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4e0e -2 \u4e0d\u540c\uff0c\u884c\u5217\u5f0f 2\u00d72 \u5c06\u4e0d\u540c\u4e8e 0\uff0c\u56e0\u6b64\u77e9\u9635\u7684\u79e9\u5c06\u4e3a 2\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-04b3447f6e823c3e11b66919654e7a5a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\color{blue} \\boxed{ \\begin{array}{c} \\\\[-2ex] \\color{black}\\phantom{33} \\bm{a \\neq -2 \\ \\longrightarrow \\ Rg(A)=2} \\phantom{33} \\\\[-2ex] &amp; \\end{array} }\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"323\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u8ba9\u6211\u4eec\u770b\u770b\u5f53<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0e72cd3ad115f5d34fb5077b4d7d278a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a=-2 :\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" 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-6ecbf63b188b46c05e67741cee83d7a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a = -2 \\longrightarrow A= \\begin{pmatrix} -1&amp;-3&amp;-2&amp;1\\\\[1.1ex] 4&amp;12&amp;8&amp;-4\\\\[1.1ex] 2&amp;6&amp;4&amp;-2 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"297\" 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<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1961b1513bd5718956433f1198aa5844_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4e3a -2\uff0c\u5219\u6240\u6709 2 \u9636\u884c\u5217\u5f0f\u5747\u4e3a 0\u3002\u56e0\u6b64\u5b83\u4e0d\u80fd\u4e3a 2 \u9636\u3002\u5e76\u4e14\u7531\u4e8e\u81f3\u5c11\u5b58\u5728\u4e00\u4e2a\u4e0d\u540c\u4e8e 0 \u7684 1\u00d71 \u884c\u5217\u5f0f\uff0c\u56e0\u6b64\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\u77e9\u9635\u7684\u79e9\u4e3a 1\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-eb1cee57ae9619b3e4fdbf2357893425_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\color{blue} \\boxed{ \\begin{array}{c} \\\\[-2ex] \\color{black} \\phantom{33} \\bm{a = -2 \\ \\longrightarrow \\ Rg(A)=1} \\phantom{33} \\\\[-2ex] &amp; \\end{array} }\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"323\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u6211\u4eec\u53d1\u73b0\u4e86\u4e24\u79cd\u60c5\u51b5\uff0c\u5176\u4e2d\u77e9\u9635 A \u7684\u8303\u56f4\u968f\u53c2\u6570\u53d6\u503c\u7684\u53d8\u5316\u800c\u53d8\u5316\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2bdfb67894431a4a08a3e791dcda0313_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\color{blue} \\boxed{ \\begin{array}{c} \\\\ \\color{black} \\phantom{33} \\bm{a \\neq -2 \\longrightarrow \\ Rg(A)=2} \\phantom{33} \\\\[3ex] \\color{black} \\bm{a = -2\\ \\longrightarrow \\ Rg(A)=1}   \\\\ &amp; \\end{array} }\" title=\"Rendered by QuickLaTeX.com\" height=\"122\" width=\"317\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u4e86\u89e3\u5982\u4f55\u6839\u636e\u53c2\u6570\u8ba1\u7b97\u8868\u7684\u6392\u540d\u3002\u60a8\u8fd8\u5c06\u627e\u5230\u5173\u4e8e\u5982\u4f55\u6839\u636e\u4e00\u4e2a\u53c2\u6570\u67e5\u627e\u77e9\u9635\u8303\u56f4\u7684\u5206\u6b65\u793a\u4f8b\u548c\u5df2\u89e3\u51b3\u7684\u7ec3 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e7%9f%a9%e9%98%b5%e7%9a%84%e8%8c%83%e5%9b%b4%e4%bd%9c%e4%b8%ba%e5%8f%82%e6%95%b0%e7%9a%84%e5%87%bd%e6%95%b0-%e7%9f%a9%e9%98%b5%e7%9a%84%e7%a4%ba%e4%be%8b%e5%92%8c%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%9a%84\/\"> <span class=\"screen-reader-text\">\u57fa\u4e8e\u53c2\u6570\u7684\u6570\u7ec4\u8303\u56f4<\/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":[4],"tags":[],"class_list":["post-292","post","type-post","status-publish","format-standard","hentry","category-4"],"yoast_head":"<!-- This site is optimized 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