{"id":291,"date":"2023-07-06T17:31:42","date_gmt":"2023-07-06T17:31:42","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e7%9f%a9%e9%98%b5%e7%9a%84%e7%a7%a9\/"},"modified":"2023-07-06T17:31:42","modified_gmt":"2023-07-06T17:31:42","slug":"%e7%9f%a9%e9%98%b5%e7%9a%84%e7%a7%a9","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e7%9f%a9%e9%98%b5%e7%9a%84%e7%a7%a9\/","title":{"rendered":"\u901a\u8fc7\u884c\u5217\u5f0f\u8ba1\u7b97\u77e9\u9635\u7684\u79e9"},"content":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u4e86\u89e3\u5b83\u662f\u4ec0\u4e48\u4ee5\u53ca\u5982\u4f55\u901a\u8fc7\u884c\u5217\u5f0f\u8ba1\u7b97<strong>\u77e9\u9635\u7684\u8303\u56f4<\/strong>\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u5c06\u627e\u5230\u793a\u4f8b\u548c\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\uff0c\u4ee5\u5b66\u4e60\u5982\u4f55\u8f7b\u677e\u627e\u5230\u77e9\u9635\u7684\u8303\u56f4\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u5c06\u770b\u5230\u77e9\u9635\u7684\u8303\u56f4\u5c5e\u6027\u3002<\/p>\n<h2 class=\"wp-block-heading\">\u77e9\u9635\u7684\u79e9\u662f\u591a\u5c11\uff1f<\/h2>\n<p>\u77e9\u9635\u7684\u503c\u57df\u5b9a\u4e49\u4e3a\uff1a<\/p>\n<p class=\"has-background\" style=\"background-color:#dff6ff\"><strong>\u77e9\u9635\u7684\u79e9<\/strong>\u662f\u884c\u5217\u5f0f\u4e0d\u4e3a0\u7684\u6700\u5927\u65b9\u5b50\u77e9\u9635\u7684\u9636\u3002<\/p>\n<p>\u5728\u672c\u9875\u4e2d\uff0c\u6211\u4eec\u5c06\u901a\u8fc7\u884c\u5217\u5f0f\u65b9\u6cd5\u4e86\u89e3\u77e9\u9635\u7684\u8303\u56f4\uff0c\u4f46\u662f\u77e9\u9635\u7684\u8303\u56f4\u4e5f\u53ef\u4ee5\u901a\u8fc7\u9ad8\u65af\u65b9\u6cd5\u786e\u5b9a\uff0c\u5c3d\u7ba1\u5b83\u66f4\u6162\u4e14\u66f4\u590d\u6742\u3002<\/p>\n<p>\u4e00\u65e6\u6211\u4eec\u77e5\u9053\u77e9\u9635\u7684\u8303\u56f4\u662f\u4ec0\u4e48\uff0c\u6211\u4eec\u5c31\u4f1a\u770b\u5230\u5982\u4f55\u901a\u8fc7\u884c\u5217\u5f0f\u627e\u5230\u77e9\u9635\u7684\u8303\u56f4\u3002\u4f46\u8bf7\u8bb0\u4f4f\uff0c\u8981\u6c42\u89e3\u77e9\u9635\u7684\u8303\u56f4\uff0c\u60a8\u9996\u5148\u9700\u8981\u77e5\u9053\u5982\u4f55\u8ba1\u7b97<a href=\"https:\/\/mathority.org\/cn\/\u884c\u5217\u5f0f-3x3-sarrus-\u89c4\u5219\u793a\u4f8b\u548c\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\/\">3&#215;3 \u884c\u5217\u5f0f<\/a>\u3002<\/p>\n<h2 class=\"wp-block-heading\">\u5982\u4f55\u77e5\u9053\u77e9\u9635\u7684\u8303\u56f4\uff1f\u4f8b\u5b50\uff1a<\/h2>\n<ul>\n<li>\u8ba1\u7b97\u4ee5\u4e0b\u7ef4\u5ea6\u4e3a 3\u00d74 \u7684\u77e9\u9635\u7684\u8303\u56f4\uff1a <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-79e80ea42079a394262a4fcce5a863f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A= \\left( \\begin{array}{cccc} 1 &amp; 3 &amp; 4 &amp; -1 \\\\[1.1ex] 0 &amp; 2 &amp; 1 &amp; -1  \\\\[1.1ex] 3 &amp; -1 &amp; 7 &amp; 2 \\end{array} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"191\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-background\" style=\"background-color:#dff6ff\">\u6211\u4eec\u603b\u662f\u9996\u5148\u5c1d\u8bd5\u901a\u8fc7\u6c42\u89e3\u9636\u7684\u6700\u5927\u884c\u5217\u5f0f\u6765\u67e5\u770b\u77e9\u9635\u662f\u5426\u5177\u6709\u6700\u5927\u79e9\u3002\u5e76\u4e14\uff0c\u5982\u679c\u8be5\u9636\u7684\u884c\u5217\u5f0f\u7b49\u4e8e 0\uff0c\u6211\u4eec\u5c06\u7ee7\u7eed\u6d4b\u8bd5\u8f83\u4f4e\u9636\u7684\u884c\u5217\u5f0f\uff0c\u76f4\u5230\u627e\u5230\u9664 0 \u4e4b\u5916\u7684\u5176\u4ed6\u884c\u5217\u5f0f\u3002<\/p>\n<p>\u5728\u672c\u4f8b\u4e2d\uff0c\u5b83\u662f\u4e00\u4e2a\u7ef4\u5ea6\u4e3a 3\u00d74 \u7684\u77e9\u9635\u3002<strong>\u56e0\u6b64\uff0c\u5b83\u6700\u591a\u4e3a 3 \u9636<\/strong>\uff0c\u56e0\u4e3a\u6211\u4eec\u65e0\u6cd5\u786e\u5b9a 4 \u9636\u7684\u4efb\u4f55\u884c\u5217\u5f0f\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u91c7\u7528\u4efb\u4f55 3\u00d73 \u5b50\u77e9\u9635\uff0c\u770b\u770b\u5b83\u7684\u884c\u5217\u5f0f\u662f\u5426\u4e3a 0\u3002\u4f8b\u5982\uff0c\u6211\u4eec\u7528\u4ee5\u4e0b\u516c\u5f0f\u6c42\u89e3\u524d 3 \u5217\u7684\u884c\u5217\u5f0f\uff1a\u8428\u9c81\u65af\u89c4\u5219\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-819aaaa272025ce70b7852d00680483d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{tabular}{cccc}\\cellcolor[HTML]{ABEBC6}1 &amp; \\cellcolor[HTML]{ABEBC6}3 &amp; \\cellcolor[HTML]{ABEBC6}4  &amp; -1 \\\\ \\cellcolor[HTML]{ABEBC6} &amp; \\cellcolor[HTML]{ABEBC6} &amp;\\cellcolor[HTML]{ABEBC6} &amp; \\\\[-2ex] \\cellcolor[HTML]{ABEBC6}0 &amp; \\cellcolor[HTML]{ABEBC6}2 &amp; \\cellcolor[HTML]{ABEBC6} 1 &amp; -1 \\\\ \\cellcolor[HTML]{ABEBC6} &amp; \\cellcolor[HTML]{ABEBC6} &amp;\\cellcolor[HTML]{ABEBC6} &amp; \\\\[-2ex]\\cellcolor[HTML]{ABEBC6} 3 &amp;\\cellcolor[HTML]{ABEBC6} -1 &amp; \\cellcolor[HTML]{ABEBC6} 7 &amp; 2                    \\end{tabular} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"76\" width=\"570\" 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-aedcd597b0cd9cd0ad11ab1d99bd0e5a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} 1 &amp; 3 &amp; 4 \\\\[1.1ex] 0 &amp; 2 &amp; 1   \\\\[1.1ex] 3 &amp; -1 &amp; 7  \\end{vmatrix} = 14 + 9 + 0 - 24 + 1 - 0 = \\bm{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"318\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u7b2c 1\u30012 \u548c 3 \u5217\u7684\u884c\u5217\u5f0f\u662f 0\u3002\u6211\u4eec\u73b0\u5728\u5fc5\u987b\u5c1d\u8bd5\u53e6\u4e00\u4e2a\u884c\u5217\u5f0f\uff0c\u4f8b\u5982\u7b2c 1\u30012 \u548c 4 \u5217\u7684\u884c\u5217\u5f0f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ddfbcde7994d5665983fda2423c82de3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{tabular}{cccc}\\cellcolor[HTML]{ABEBC6}1 &amp; \\cellcolor[HTML]{ABEBC6} 3 &amp; 4  &amp; \\cellcolor[HTML]{ABEBC6}-1 \\\\ \\cellcolor[HTML]{ABEBC6} &amp; \\cellcolor[HTML]{ABEBC6} &amp; &amp; \\cellcolor[HTML]{ABEBC6} \\\\[-2ex] \\cellcolor[HTML]{ABEBC6}0 &amp;\\cellcolor[HTML]{ABEBC6}2 &amp; 1 &amp; \\cellcolor[HTML]{ABEBC6} -1 \\\\ \\cellcolor[HTML]{ABEBC6} &amp; \\cellcolor[HTML]{ABEBC6}&amp; &amp; \\cellcolor[HTML]{ABEBC6} \\\\[-2ex]\\cellcolor[HTML]{ABEBC6} 3 &amp; \\cellcolor[HTML]{ABEBC6}-1 &amp; 7 &amp; \\cellcolor[HTML]{ABEBC6}2                    \\end{tabular} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"76\" width=\"565\" 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-6f13263d4697369ed7d98bf7f972d15f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} 1 &amp; 3 &amp; -1 \\\\[1.1ex] 0 &amp; 2 &amp; -1   \\\\[1.1ex] 3 &amp; -1 &amp; 2  \\end{vmatrix} = 4 -9 + 0 + 6-1 - 0 = \\bm{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"314\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u5b83\u8fd8\u7ed9\u4e86\u6211\u4eec 0\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u7ee7\u7eed\u6d4b\u8bd5 3 \u9636\u7684\u884c\u5217\u5f0f\uff0c\u770b\u770b\u662f\u5426\u5b58\u5728\u9664 0 \u4e4b\u5916\u7684\u5176\u4ed6\u884c\u5217\u5f0f\u3002\u6211\u4eec\u73b0\u5728\u6d4b\u8bd5\u7531\u7b2c 1\u30013 \u548c 4 \u5217\u5f62\u6210\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-2682212fc905820bb8c2c2b73eeb49e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{tabular}{cccc}\\cellcolor[HTML]{ABEBC6}1 &amp; 3 &amp; \\cellcolor[HTML]{ABEBC6}4  &amp; \\cellcolor[HTML]{ABEBC6}-1 \\\\ \\cellcolor[HTML]{ABEBC6} &amp; &amp;\\cellcolor[HTML]{ABEBC6} &amp; \\cellcolor[HTML]{ABEBC6} \\\\[-2ex] \\cellcolor[HTML]{ABEBC6}0 &amp;2 &amp; \\cellcolor[HTML]{ABEBC6} 1 &amp; \\cellcolor[HTML]{ABEBC6} -1 \\\\ \\cellcolor[HTML]{ABEBC6} &amp;  &amp;\\cellcolor[HTML]{ABEBC6} &amp; \\cellcolor[HTML]{ABEBC6} \\\\[-2ex]\\cellcolor[HTML]{ABEBC6} 3 &amp;  -1 &amp; \\cellcolor[HTML]{ABEBC6} 7 &amp; \\cellcolor[HTML]{ABEBC6}2                    \\end{tabular} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"76\" width=\"570\" 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-c84fbf30f1005e0bdd6496369c68efb4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} 1 &amp; 4 &amp; -1 \\\\[1.1ex] 0 &amp; 1 &amp; -1   \\\\[1.1ex] 3 &amp; 7 &amp; 2  \\end{vmatrix} = 2 -12+0 +3 +7- 0 = \\bm{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"309\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u5728 3 \u9636\u884c\u5217\u5f0f\u4e2d\uff0c\u53ea\u9700\u5c1d\u8bd5\u7531\u7b2c 2\u30013 \u548c 4 \u5217\u7ec4\u6210\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-610e7befed3409c44ad1b84a6c84605d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{tabular}{cccc}1 &amp; \\cellcolor[HTML]{ABEBC6}3 &amp; \\cellcolor[HTML]{ABEBC6}4  &amp; \\cellcolor[HTML]{ABEBC6}-1 \\\\  &amp; \\cellcolor[HTML]{ABEBC6} &amp;\\cellcolor[HTML]{ABEBC6} &amp; \\cellcolor[HTML]{ABEBC6} \\\\[-2ex] 0 &amp; \\cellcolor[HTML]{ABEBC6}2 &amp; \\cellcolor[HTML]{ABEBC6} 1 &amp; \\cellcolor[HTML]{ABEBC6} -1 \\\\  &amp; \\cellcolor[HTML]{ABEBC6} &amp;\\cellcolor[HTML]{ABEBC6} &amp; \\cellcolor[HTML]{ABEBC6} \\\\[-2ex] 3 &amp; \\cellcolor[HTML]{ABEBC6} -1 &amp; \\cellcolor[HTML]{ABEBC6} 7 &amp; \\cellcolor[HTML]{ABEBC6}2                    \\end{tabular} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"76\" width=\"570\" 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-6377c641072d9eba07fd2b9670ffbf50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle   \\begin{vmatrix} 3 &amp; 4 &amp; -1 \\\\[1.1ex]  2 &amp; 1 &amp; -1  \\\\[1.1ex] -1 &amp; 7 &amp; 2 \\end{vmatrix} = 6+4-14-1+21-16 = \\bm{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"341\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u5df2\u7ecf\u5c1d\u8bd5\u4e86\u77e9\u9635 A \u7684\u6240\u6709\u53ef\u80fd\u7684 3&#215;3 \u884c\u5217\u5f0f\uff0c\u5e76\u4e14\u7531\u4e8e\u8fd9\u4e9b\u884c\u5217\u5f0f\u90fd\u4e0d\u4e0e 0 \u4e0d\u540c\uff0c<strong>\u56e0\u6b64\u8be5\u77e9\u9635\u4e0d\u662f 3 \u9636\u7684<\/strong>\u3002\u56e0\u6b64\uff0c\u6700\u591a\u53ea\u80fd\u662f\u6392\u540d2\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-157fd11377c30ccf66e64960e295866b_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>\u73b0\u5728\u6211\u4eec\u5c06\u770b\u770b\u8be5\u77e9\u9635\u662f\u5426\u4e3a 2 \u9636\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u5fc5\u987b\u627e\u5230\u4e00\u4e2a\u884c\u5217\u5f0f\u4e0d\u4e3a 0 \u7684 2 \u9636\u65b9\u5b50\u77e9\u9635\u3002\u6211\u4eec\u5c06\u5c1d\u8bd5\u5de6\u4e0a\u89d2\u7684 2\u00d72 \u5b50\u77e9\u9635\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b0ae4ab76e4e45bbb1aecd49af2523a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( \\begin{tabular}{cccc}\\cellcolor[HTML]{ABEBC6}1 &amp; \\cellcolor[HTML]{ABEBC6}3 &amp; 4  &amp; -1 \\\\ \\cellcolor[HTML]{ABEBC6} &amp; \\cellcolor[HTML]{ABEBC6} &amp; &amp; \\\\[-2ex] \\cellcolor[HTML]{ABEBC6}0 &amp; \\cellcolor[HTML]{ABEBC6}2 &amp;  1 &amp; -1 &amp;  &amp; &amp; \\\\[-2ex] 3 &amp; -1 &amp;  7 &amp; 2                    \\end{tabular} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"75\" width=\"411\" 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-3320ea7301733c03681caf31e7539b25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\begin{vmatrix} 1 &amp; 3 \\\\[1.1ex] 0 &amp; 2  \\end{vmatrix} = 2-0 = 2 \\bm{ \\neq 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"167\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u5728\u77e9\u9635\u4e2d\u53d1\u73b0\u4e86\u4e00\u4e2a\u4e0d\u540c\u4e8e 0 \u7684 2 \u9636\u884c\u5217\u5f0f\u3002\u56e0\u6b64\uff0c<strong>\u77e9\u9635\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-c40408b072a81f61800b6521c3ede2cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{rg(A)=2}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"76\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\">\u5df2\u89e3\u51b3\u7684\u77e9\u9635\u8303\u56f4\u95ee\u9898<\/h2>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u786e\u5b9a\u4ee5\u4e0b 2\u00d72 \u77e9\u9635\u7684\u79e9\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ca5f88e86382a14720247e910084095c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\begin{pmatrix} 3 &amp; 1 \\\\[1.1ex] 5 &amp; 6  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"95\" 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\u8ba1\u7b97\u6574\u4e2a\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-88be02e3f0e84b30178b811354994424_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} A \\end{vmatrix}=\\begin{vmatrix} 3 &amp; 1 \\\\[1.1ex] 5 &amp; 6 \\end{vmatrix} = 18-5 = 13 \\bm{\\neq 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"233\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u53d1\u73b0\u4e86\u4e00\u4e2a\u4e0d\u540c\u4e8e0\u76842\u9636\u884c\u5217\u5f0f\u3002\u56e0\u6b64\uff0c<strong>\u8be5\u77e9\u9635\u7684\u79e9\u4e3a2\u3002<\/strong> <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c40408b072a81f61800b6521c3ede2cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{rg(A)=2}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"76\" style=\"vertical-align: -5px;\"><\/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>\u6c42\u4ee5\u4e0b\u7ef4\u5ea6\u4e3a 2 \u00d7 2 \u7684\u77e9\u9635\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-19dde855da87ad73bdec3135fca04e78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\begin{pmatrix} 2 &amp; 3 \\\\[1.1ex] 4 &amp; 6  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"95\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u9996\u5148\uff0c\u6211\u4eec\u6c42\u89e3\u6574\u4e2a\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-eb383f77013e752e0f22ad582dbd3c80_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} A \\end{vmatrix}=\\begin{vmatrix} 2 &amp; 3 \\\\[1.1ex] 4 &amp; 6 \\end{vmatrix} = 12-12 \\bm{=0}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"201\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u552f\u4e00\u53ef\u80fd\u7684 2\u00d72 \u884c\u5217\u5f0f\u7ed9\u51fa 0\uff0c\u56e0\u6b64\u8be5\u77e9\u9635\u4e0d\u662f 2 \u9636\u7684\u3002<\/p>\n<p class=\"has-text-align-left\">\u4f46\u77e9\u9635\u5185\u90e8\u8fd8\u6709 0 \u4ee5\u5916\u7684 1&#215;1 \u884c\u5217\u5f0f\uff0c\u4f8b\u5982\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9bfea6551282e7213ca85662eb657b6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} 2  \\end{vmatrix} = 2 \\bm{\\neq 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"79\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"><strong>\u56e0\u6b64\u8be5\u77e9\u9635\u7684\u79e9\u4e3a 1\u3002<\/strong> <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e9b93965a2d6e8834b62367fbe854e02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{rg(A)=1}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"76\" style=\"vertical-align: -5px;\"><\/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>\u4e0b\u9762\u7684 3&#215;3 \u65b9\u9635\u7684\u8303\u56f4\u662f\u591a\u5c11\uff1f <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fbe69cc53a58fd72117fa4aaa7a0ec38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\begin{pmatrix} 1 &amp; -3 &amp; 2 \\\\[1.1ex] 2 &amp; 1 &amp; 4 \\\\[1.1ex] 1 &amp; 4 &amp; 2 \\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\">\u9996\u5148\u7528Sarrus\u89c4\u5219\u8ba1\u7b97\u6574\u4e2a\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-a1bda19a46e006dfc43ade0e92f189e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} A \\end{vmatrix}= \\begin{vmatrix} 1 &amp; -3 &amp; 2 \\\\[1.1ex] 2 &amp; 1 &amp; 4 \\\\[1.1ex] 1 &amp; 4 &amp; 2 \\end{vmatrix} = 2-12+16-2-16+12 \\bm{=0}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"380\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u552f\u4e00\u53ef\u80fd\u7684 3\u00d73 \u884c\u5217\u5f0f\u7ed9\u51fa 0\uff0c\u56e0\u6b64\u8be5\u77e9\u9635\u4e0d\u662f 3 \u9636\u7684\u3002<\/p>\n<p class=\"has-text-align-left\">\u4f46\u77e9\u9635\u5185\u8fd8\u6709\u9664 0 \u4e4b\u5916\u7684 2 \u9636\u884c\u5217\u5f0f\uff0c\u4f8b\u5982\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9a1e82c35249f351ba9513437da95c65_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} 1 &amp; -3 \\\\[1.1ex] 2 &amp; 1  \\end{vmatrix} = 1 +6 = 7 \\bm{\\neq 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"181\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c<strong>\u8be5\u77e9\u9635\u7684\u79e9\u4e3a 2<\/strong> \u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c40408b072a81f61800b6521c3ede2cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{rg(A)=2}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"76\" style=\"vertical-align: -5px;\"><\/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>\u8ba1\u7b97\u4ee5\u4e0b 3 \u9636\u77e9\u9635\u7684\u79e9\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7d952325e084adb3fa3b97c7fc10c1ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\begin{pmatrix} 3 &amp; -1 &amp; 1 \\\\[1.1ex] 4 &amp; -2 &amp; 3 \\\\[1.1ex] 2 &amp; 5 &amp; 2 \\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\">\u9996\u5148\u7528Sarrus\u89c4\u5219\u6c42\u89e3\u6574\u4e2a\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-819e9bea5c6d6d536a4dafba325ae45e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} A \\end{vmatrix}= \\begin{vmatrix} 3 &amp; -1 &amp; 1 \\\\[1.1ex] 4 &amp; -2 &amp; 3 \\\\[1.1ex] 2 &amp; 5 &amp; 2 \\end{vmatrix} = -12-6+20+4-45+8 =  -31\\bm{ \\neq0}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"440\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6574\u4e2a\u77e9\u9635\u7684\u884c\u5217\u5f0f\u7684\u8ba1\u7b97\u7ed3\u679c\u4e0d\u662f 0\u3002\u56e0\u6b64\uff0c\u8be5\u77e9\u9635\u5177\u6709\u6700\u5927\u79e9\uff0c\u5373<strong>\u79e9 3\u3002<\/strong> <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8548c1b53b3e4fbb5509589cb60f87b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{rg(A)=3}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"77\" style=\"vertical-align: -5px;\"><\/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>\u4ee5\u4e0b 3 \u9636\u77e9\u9635\u7684\u79e9\u662f\u591a\u5c11\uff1f <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d90091dd51727e806e6788a9594735ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\begin{pmatrix} 2 &amp; 5 &amp; -1 \\\\[1.1ex] 3 &amp; -2 &amp; -4 \\\\[1.1ex] 5 &amp; 3 &amp; -5 \\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\">\u9996\u5148\u7528Sarrus\u89c4\u5219\u8ba1\u7b97\u6574\u4e2a\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-e4eee911dcf234c3fa63177e533901af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} A \\end{vmatrix}= \\begin{vmatrix}2 &amp; 5 &amp; -1 \\\\[1.1ex] 3 &amp; -2 &amp; -4 \\\\[1.1ex] 5 &amp; 3 &amp; -5 \\end{vmatrix} =20-100-9-10+24+75 \\bm{= 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"411\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u552f\u4e00\u53ef\u80fd\u7684 3\u00d73 \u884c\u5217\u5f0f\u7ed9\u51fa 0\uff0c\u56e0\u6b64\u8be5\u77e9\u9635\u4e0d\u662f 3 \u9636\u7684\u3002<\/p>\n<p class=\"has-text-align-left\">\u4f46\u77e9\u9635\u5185\u90e8\u9664\u4e86 0 \u4e4b\u5916\u8fd8\u6709 2 \u00d7 2 \u4e2a\u884c\u5217\u5f0f\uff0c\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-1397b7f935df1c8cce082c3f2f1418d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} 2 &amp; 5 \\\\[1.1ex] 3 &amp; -2  \\end{vmatrix} = -4-15 = -19\\bm{\\neq 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"226\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"><strong>\u56e0\u6b64\u8be5\u77e9\u9635\u7684\u79e9\u4e3a 2<\/strong> \u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c40408b072a81f61800b6521c3ede2cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{rg(A)=2}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"76\" style=\"vertical-align: -5px;\"><\/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-118\"><\/div>\n<\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e606<\/h3>\n<p>\u6c42\u4ee5\u4e0b 3&#215;4 \u77e9\u9635\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-46ff20ee9ee9e4fac3e8858c55961f8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\begin{pmatrix} 3 &amp; 2 &amp; -4 &amp; 1 \\\\[1.1ex] 2 &amp; -2 &amp; -3 &amp; 5 \\\\[1.1ex] 5 &amp; 0 &amp; -7 &amp; 3 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"175\" 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\">\u8be5\u77e9\u9635\u4e0d\u80fd\u4e3a 4 \u9636\uff0c\u56e0\u4e3a\u6211\u4eec\u65e0\u6cd5\u751f\u6210 4\u00d74 \u884c\u5217\u5f0f\u3002\u90a3\u4e48\u6211\u4eec\u901a\u8fc7\u8ba1\u7b97 3\u00d73 \u884c\u5217\u5f0f\u6765\u770b\u770b\u5b83\u662f\u5426\u662f 3 \u9636\u7684\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-2897851f49a9556fc03aded5f1495297_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} A \\end{vmatrix}= \\begin{vmatrix}3 &amp; 2 &amp; -4  \\\\[1.1ex] 2 &amp; -2 &amp; -3  \\\\[1.1ex] 5 &amp; 0 &amp; -7 \\end{vmatrix} =42-30+0-40-0+28 \\bm{= 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"393\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u524d 3 \u5217\u7684\u884c\u5217\u5f0f\u7ed9\u51fa 0\u3002\u4f46\u662f\uff0c\u540e 3 \u5217\u7684\u884c\u5217\u5f0f\u7ed9\u51fa 0 \u4ee5\u5916\u7684\u503c\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c0821770a710807269d81fb1f8dd21a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} 2 &amp; -4 &amp; 1 \\\\[1.1ex] -2 &amp; -3 &amp; 5 \\\\[1.1ex] 0 &amp; -7 &amp; 3  \\end{vmatrix} = -18+0+14-0+70-24 = 42 \\bm{\\neq 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"400\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u7531\u4e8e\u5185\u90e8\u6709\u4e00\u4e2a\u884c\u5217\u5f0f\u4e0d\u4e3a0\u76843\u9636\u5b50\u77e9\u9635\uff0c<strong>\u56e0\u6b64\u8be5\u77e9\u9635\u7684\u79e9\u4e3a3<\/strong> \u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8548c1b53b3e4fbb5509589cb60f87b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{rg(A)=3}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"77\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e607<\/h3>\n<p>\u8ba1\u7b97\u4ee5\u4e0b 4&#215;3 \u77e9\u9635\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-83e7cebc0d95d73f653cf54bd316c4f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\begin{pmatrix} 1 &amp; -3 &amp; -2 \\\\[1.1ex] 3 &amp; 4 &amp; -5  \\\\[1.1ex] 5 &amp; -2 &amp; -9  \\\\[1.1ex] -2 &amp; -7 &amp; 3\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"164\" 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\">\u8be5\u77e9\u9635\u4e0d\u80fd\u4e3a 4 \u9636\uff0c\u56e0\u4e3a\u6211\u4eec\u65e0\u6cd5\u89e3\u6790\u4efb\u4f55 4\u00d74 \u884c\u5217\u5f0f\u3002\u56e0\u6b64\uff0c\u8ba9\u6211\u4eec\u901a\u8fc7\u6267\u884c\u6240\u6709\u53ef\u80fd\u7684 3&#215;3 \u884c\u5217\u5f0f\u6765\u770b\u770b\u5b83\u662f\u5426\u4e3a 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-1eec1befc1515b4405529ede01c55618_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} 1 &amp; -3 &amp; -2 \\\\[1.1ex] 3 &amp; 4 &amp; -5 \\\\[1.1ex] 5 &amp; -2 &amp; -9\\end{vmatrix} \\bm{= 0} \\qquad \\begin{vmatrix} 1 &amp; -3 &amp; -2 \\\\[1.1ex] 5 &amp; -2 &amp; -9 \\\\[1.1ex] -2 &amp; -7 &amp; 3\\end{vmatrix} \\bm{= 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"308\" 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-fa1de344c0bb747c9861afd4de5fa7c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} 1 &amp; -3 &amp; -2 \\\\[1.1ex] 3 &amp; 4 &amp; -5 \\\\[1.1ex] -2 &amp; -7 &amp; 3\\end{vmatrix} \\bm{= 0} \\qquad \\begin{vmatrix} 3 &amp; 4 &amp; -5 \\\\[1.1ex] 5 &amp; -2 &amp; -9 \\\\[1.1ex] -2 &amp; -7 &amp; 3\\end{vmatrix} \\bm{= 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"322\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7531\u4e8e\u6240\u6709\u53ef\u80fd\u7684 3\u00d73 \u884c\u5217\u5f0f\u90fd\u4e3a 0\uff0c\u56e0\u6b64\u8be5\u77e9\u9635\u4e5f\u4e0d\u662f 3 \u9636\u7684\u3002\u6211\u4eec\u73b0\u5728\u5c1d\u8bd5 2\u00d72 \u884c\u5217\u5f0f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-981d085760dd1b1dd46aab17f1d7ba78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} 1 &amp; -3 \\\\[1.1ex] 3 &amp; 4  \\end{vmatrix} =13 \\bm{\\neq 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"127\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7531\u4e8e\u77e9\u9635 A \u5185\u5b58\u5728\u4e00\u4e2a\u884c\u5217\u5f0f\u4e0d\u4e3a 0 \u7684 2 \u9636\u5b50\u77e9\u9635\uff0c<strong>\u56e0\u6b64\u8be5\u77e9\u9635\u7684\u79e9\u4e3a 2<\/strong> \u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c40408b072a81f61800b6521c3ede2cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{rg(A)=2}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"76\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e608<\/h3>\n<p>\u6c42\u4ee5\u4e0b 4 \u00d7 4 \u77e9\u9635\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-bd5abef80b8d6ae74d4d60a0cf11e3ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\begin{pmatrix} 2 &amp; 0 &amp; 1 &amp; -1  \\\\[1.1ex] 3 &amp; 1 &amp; 1 &amp; -1  \\\\[1.1ex] 4 &amp; -2 &amp; -1 &amp; 3  \\\\[1.1ex] -1 &amp; 3 &amp; 2 &amp;  -4\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" 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\">\u6211\u4eec\u5fc5\u987b\u6c42\u89e3\u6574\u4e2a\u77e9\u9635\u7684\u884c\u5217\u5f0f\uff0c\u770b\u770b\u5b83\u662f\u5426\u662f 4 \u9636\u7684\u3002<\/p>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u6c42\u89e3 4&#215;4 \u884c\u5217\u5f0f\uff0c\u60a8\u5fc5\u987b\u9996\u5148\u5bf9\u884c\u8fdb\u884c\u8fd0\u7b97\uff0c\u5c06\u5217\u4e2d\u9664\u4e00\u4e2a\u5143\u7d20\u4e4b\u5916\u7684\u6240\u6709\u5143\u7d20\u8f6c\u6362\u4e3a\u96f6\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-27642038b0dc0358b382aaeab5c55263_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{vmatrix} 2 &amp; 0 &amp; 1 &amp; -1 \\\\[1.1ex] 3 &amp; 1 &amp; 1 &amp; -1 \\\\[1.1ex] 4 &amp; -2 &amp; -1 &amp; 3 \\\\[1.1ex] -1 &amp; 3 &amp; 2 &amp; -4 \\end{vmatrix} \\begin{matrix} \\\\[1.1ex]  \\\\[1.1ex]\\xrightarrow{f_3 + 2f_2} \\\\[1.1ex] \\xrightarrow{f_4 - 3f_2} \\end{matrix} \\begin{vmatrix} 2 &amp; 0 &amp; 1 &amp; -1 \\\\[1.1ex] 3 &amp; 1 &amp; 1 &amp; -1 \\\\[1.1ex] 10 &amp; 0 &amp; 1 &amp; 1 \\\\[1.1ex] -10 &amp; 0 &amp; -1 &amp; -1 \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"111\" width=\"360\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u73b0\u5728\u8ba1\u7b97\u4ee3\u8868\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-239ee8aebdd8161e1e86d3d093ade490_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{vmatrix} 2 &amp; 0 &amp; 1 &amp; -1 \\\\[1.1ex] 3 &amp; 1 &amp; 1 &amp; -1 \\\\[1.1ex] 10 &amp; 0 &amp; 1 &amp; 1 \\\\[1.1ex] -10 &amp; 0 &amp; -1 &amp; -1 \\end{vmatrix} \\displaystyle = 0\\bm{\\cdot} \\text{Adj(0)} +1\\bm{\\cdot} \\text{Adj(1)} +0\\bm{\\cdot} \\text{Adj(0)} + 0\\bm{\\cdot} \\text{Adj(0)}\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"492\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u7b80\u5316\u4e00\u4e0b\u672f\u8bed\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-cd7140ff98995310b9c70e27c89dba05_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"=\\cancel{0\\bm{\\cdot} \\text{Adj(0)}}+1\\bm{\\cdot} \\text{Adj(1)} +\\cancel{0\\bm{\\cdot} \\text{Adj(0)}} + \\cancel{0\\bm{\\cdot} \\text{Adj(0)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"343\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-029594698d2ffb9e165ed06c51bd495e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"= \\text{Adj(1)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"69\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u8ba1\u7b97 1 \u7684\u4f34\u968f\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-b30414c1569334502b1f17ee5380bd4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle = (-1)^{2+2} \\begin{vmatrix}2 &amp;  1 &amp; -1 \\\\[1.1ex] 10 &amp; 1 &amp; 1 \\\\[1.1ex] -10 &amp; -1 &amp; -1\\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"202\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\uff0c\u6211\u4eec\u7528 Sarrus \u89c4\u5219\u548c\u8ba1\u7b97\u5668\u8ba1\u7b97 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-15b1857a0769672f75e0ba922e34413a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle = (-1)^{4} \\cdot \\bigl[-2-10+10-10+2+10 \\bigr]\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"298\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f1b44afd86030388f2b3eb74f2117708_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle = 1 \\cdot \\bigl[0 \\bigr]\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"61\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e0f707524d15b7f3351b2e331ca447cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle = \\bm{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"28\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6574\u4e2a\u77e9\u9635\u7684 4&#215;4 \u884c\u5217\u5f0f\u7ed9\u51fa 0\uff0c\u56e0\u6b64\u77e9\u9635 A \u4e0d\u4f1a\u662f 4 \u9636\u3002\u73b0\u5728\u8ba9\u6211\u4eec\u770b\u770b\u5b83\u5185\u90e8\u662f\u5426\u6709\u9664 0 \u4e4b\u5916\u7684 3&#215;3 \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-8a8dabdc8197de8102d9e0c50db837a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} 2 &amp; 0 &amp; 1  \\\\[1.1ex] 3 &amp; 1 &amp; 1  \\\\[1.1ex] 4 &amp; -2 &amp; -1  \\end{vmatrix} = -2+0-6-4+4-0=8 \\bm{\\neq 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"355\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"><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-8548c1b53b3e4fbb5509589cb60f87b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\bm{rg(A)=3}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"77\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h2 class=\"estil_titol_H2 wp-block-heading\">\u77e9\u9635\u8303\u56f4\u5c5e\u6027<\/h2>\n<ul>\n<li>\u5982\u679c\u6211\u4eec\u5220\u9664\u586b\u5145 0 \u7684\u884c\u3001\u5217\u6216\u586b\u5145 0 \u7684\u884c\uff0c\u5219\u8303\u56f4\u4e0d\u4f1a\u88ab\u4fee\u6539\u3002<\/li>\n<\/ul>\n<ul>\n<li>\u5982\u679c\u6211\u4eec\u6539\u53d8\u4e24\u4e2a\u5e73\u884c\u884c\u7684\u987a\u5e8f\uff0c\u65e0\u8bba\u5b83\u4eec\u662f\u884c\u8fd8\u662f\u5217\uff0c\u77e9\u9635\u7684\u8303\u56f4\u4e0d\u4f1a\u6539\u53d8\u3002<\/li>\n<\/ul>\n<ul>\n<li>\u77e9\u9635\u7684\u79e9\u4e0e\u5176\u8f6c\u7f6e\u7684\u79e9\u76f8\u540c\u3002<\/li>\n<\/ul>\n<ul>\n<li>\u5982\u679c\u5c06\u884c\u6216\u5217\u4e58\u4ee5 0 \u4ee5\u5916\u7684\u6570\u5b57\uff0c\u5219\u77e9\u9635\u7684\u79e9\u4e0d\u4f1a\u6539\u53d8\u3002<\/li>\n<\/ul>\n<ul>\n<li>\u5f53\u6211\u4eec\u6d88\u9664\u4e0e\u5b83\u5e73\u884c\u7684\u5176\u4ed6\u7ebf\u7684\u7ebf\u6027\u7ec4\u5408\u7684\u7ebf\uff08\u884c\u6216\u5217\uff09\u65f6\uff0c\u8272\u8c03\u7684\u8303\u56f4\u4e0d\u4f1a\u6539\u53d8\u3002<\/li>\n<\/ul>\n<ul>\n<li>\u5982\u679c\u6211\u4eec\u6dfb\u52a0\u4e0e\u4efb\u610f\u884c\uff08\u884c\u6216\u5217\uff09\u5e73\u884c\u7684\u5176\u4ed6\u884c\u4e58\u4ee5\u4efb\u610f\u6570\u5b57\uff0c\u5219\u77e9\u9635\u7684\u8303\u56f4\u4e0d\u4f1a\u6539\u53d8\u3002\u8fd9\u5c31\u662f\u4e3a\u4ec0\u4e48\u77e9\u9635\u7684\u79e9\u4e5f\u53ef\u4ee5\u901a\u8fc7\u9ad8\u65af\u65b9\u6cd5\u8ba1\u7b97\u3002 <\/li>\n<\/ul>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div 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