{"id":21497,"date":"2025-08-21T22:00:55","date_gmt":"2025-08-21T14:00:55","guid":{"rendered":"https:\/\/blog.iyatt.com\/?p=21497"},"modified":"2025-09-18T21:56:30","modified_gmt":"2025-09-18T13:56:30","slug":"%e8%a1%8c%e5%88%97%e5%bc%8f%e5%9f%ba%e7%a1%80","status":"publish","type":"post","link":"https:\/\/blog.iyatt.com\/?p=21497","title":{"rendered":"\u884c\u5217\u5f0f\u57fa\u7840"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 ez-toc-wrap-center counter-hierarchy ez-toc-counter ez-toc-light-blue ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title ez-toc-toggle\" style=\"cursor:pointer\">\u76ee\u5f55<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span 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href=\"https:\/\/blog.iyatt.com\/?p=21497\/#%E6%A6%82%E5%BF%B5\" >\u6982\u5ff5<\/a><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/blog.iyatt.com\/?p=21497\/#%E9%80%86%E5%BA%8F\" >\u9006\u5e8f<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/blog.iyatt.com\/?p=21497\/#%E9%80%86%E5%BA%8F%E6%95%B0\" >\u9006\u5e8f\u6570<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/blog.iyatt.com\/?p=21497\/#%E8%A1%8C%E5%88%97%E5%BC%8F\" >\u884c\u5217\u5f0f<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/blog.iyatt.com\/?p=21497\/#%E4%BD%99%E5%AD%90%E5%BC%8F\" >\u4f59\u5b50\u5f0f<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/blog.iyatt.com\/?p=21497\/#%E8%A1%8C%E5%88%97%E5%BC%8F%E8%AE%A1%E7%AE%97\" >\u884c\u5217\u5f0f\u8ba1\u7b97<\/a><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/blog.iyatt.com\/?p=21497\/#%E4%BA%8C%E9%98%B6%E8%A1%8C%E5%88%97%E5%BC%8F%E9%80%9A%E7%94%A8%E8%AE%A1%E7%AE%97%E6%96%B9%E6%B3%95\" >\u4e8c\u9636\u884c\u5217\u5f0f\u901a\u7528\u8ba1\u7b97\u65b9\u6cd5<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/blog.iyatt.com\/?p=21497\/#%E4%B8%89%E9%98%B6%E8%A1%8C%E5%88%97%E5%BC%8F%E9%80%9A%E7%94%A8%E8%AE%A1%E7%AE%97%E6%96%B9%E6%B3%95\" >\u4e09\u9636\u884c\u5217\u5f0f\u901a\u7528\u8ba1\u7b97\u65b9\u6cd5<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/blog.iyatt.com\/?p=21497\/#%E5%AF%B9%E8%A7%92%E3%80%81%E4%B8%8A%EF%BC%88%E4%B8%8B%EF%BC%89%E4%B8%89%E8%A7%92%E8%A1%8C%E5%88%97%E5%BC%8F%E8%AE%A1%E7%AE%97%E6%96%B9%E6%B3%95\" >\u5bf9\u89d2\u3001\u4e0a\uff08\u4e0b\uff09\u4e09\u89d2\u884c\u5217\u5f0f\u8ba1\u7b97\u65b9\u6cd5<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/blog.iyatt.com\/?p=21497\/#%E8%8C%83%E5%BE%B7%E8%92%99%E8%A1%8C%E5%88%97%E5%BC%8F%E8%AE%A1%E7%AE%97\" >\u8303\u5fb7\u8499\u884c\u5217\u5f0f\u8ba1\u7b97<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/blog.iyatt.com\/?p=21497\/#%E5%88%86%E5%9D%97%E8%A1%8C%E5%88%97%E5%BC%8F\" >\u5206\u5757\u884c\u5217\u5f0f<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/blog.iyatt.com\/?p=21497\/#%E8%A1%8C%E5%88%97%E5%BC%8F%E5%8F%98%E6%8D%A2%E6%80%A7%E8%B4%A8\" >\u884c\u5217\u5f0f\u53d8\u6362\u6027\u8d28<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/blog.iyatt.com\/?p=21497\/#%E8%A1%8C%E5%88%97%E5%BC%8F%E9%99%8D%E9%98%B6%E6%80%A7%E8%B4%A8\" >\u884c\u5217\u5f0f\u964d\u9636\u6027\u8d28<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h1><span class=\"ez-toc-section\" id=\"%E6%A6%82%E5%BF%B5\"><\/span>\u6982\u5ff5<span class=\"ez-toc-section-end\"><\/span><\/h1>\n<h2><span class=\"ez-toc-section\" id=\"%E9%80%86%E5%BA%8F\"><\/span>\u9006\u5e8f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8bbe i\u3001j \u662f\u4e00\u5bf9\u4e0d\u7b49\u7684\u6b63\u6574\u6570\uff0c\u82e5 i &gt; j\uff0c\u5219\u79f0 (i, j) \u4e3a\u4e00\u5bf9\u9006\u5e8f\u3002<\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E9%80%86%E5%BA%8F%E6%95%B0\"><\/span>\u9006\u5e8f\u6570<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4f8b\uff1a\u6c42 421635 \u7684\u9006\u5e8f\u6570\uff0c\u5373 <code class=\"katex-inline\">\\tau(421635)<\/code><br \/>\n\u24604&gt;2\u30014&gt;1\u30014&gt;3 \u6709 3 \u4e2a\u9006\u5e8f<br \/>\n\u24612&gt;1 \u6709 1 \u4e2a\u9006\u5e8f<br \/>\n\u24621 \u4e0d\u5927\u4e8e\u5b83\u53f3\u4fa7\u7684\u4efb\u4f55\u6570\uff0c\u6709 0 \u4e2a\u9006\u5e8f<br \/>\n\u24636&gt;3\u30016&gt;5 \u6709 2 \u4e2a\u9006\u5e8f<br \/>\n\u24643 \u4e0d\u5927\u4e8e\u5b83\u53f3\u4fa7\u7684 5\uff0c\u6709 0 \u4e2a\u9006\u5e8f<br \/>\n\u5219<code class=\"katex-inline\">\\tau(421635)<\/code>=3+1+0+2+0=6<\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E8%A1%8C%E5%88%97%E5%BC%8F\"><\/span>\u884c\u5217\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><code class=\"katex-inline\">n\\times n<\/code>\u4e2a\u6570\u7ec4\u6210\u7684\u65b9\u9635<\/p>\n<pre><code class=\"language-katex\">D=\n\\left |\n\\begin{matrix}\na_{11}&amp;a_{12}&amp;\\cdots&amp;a_{1n} \\\\\na_{21}&amp;a_{22}&amp;\\cdots&amp;a_{2n} \\\\\n\\vdots&amp;\\vdots&amp;\\vdots&amp;\\vdots \\\\\na_{n1}&amp;a_{n2}&amp;\\cdots&amp;a_{nn} \\\\\n\\end{matrix}\n\\right |<\/code><\/pre>\n<h2><span class=\"ez-toc-section\" id=\"%E4%BD%99%E5%AD%90%E5%BC%8F\"><\/span>\u4f59\u5b50\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><code class=\"katex-inline\">a_{ij}<\/code>\u7684\u4f59\u5b50\u5f0f\u8868\u793a\u4e3a<code class=\"katex-inline\">M_{ij}<\/code>\uff0c\u7531\u539f\u77e9\u9635\u53bb\u9664\u7b2c i \u884c\u548c\u7b2c j \u5217\u540e\u5269\u4f59\u90e8\u5206\u7ec4\u6210\u7684\u65b0\u7684\u884c\u5217\u5f0f\u3002<br \/>\n<code class=\"katex-inline\">a_{ij}<\/code>\u7684\u4ee3\u6570\u4f59\u5b50\u5f0f\u8868\u793a\u4e3a<code class=\"katex-inline\">A_{ij}<\/code>\uff0c<code class=\"katex-inline\">A_{ij}=(-1)^{i+j}M_{ij}<\/code><\/p>\n<h1><span class=\"ez-toc-section\" id=\"%E8%A1%8C%E5%88%97%E5%BC%8F%E8%AE%A1%E7%AE%97\"><\/span>\u884c\u5217\u5f0f\u8ba1\u7b97<span class=\"ez-toc-section-end\"><\/span><\/h1>\n<h2><span class=\"ez-toc-section\" id=\"%E4%BA%8C%E9%98%B6%E8%A1%8C%E5%88%97%E5%BC%8F%E9%80%9A%E7%94%A8%E8%AE%A1%E7%AE%97%E6%96%B9%E6%B3%95\"><\/span>\u4e8c\u9636\u884c\u5217\u5f0f\u901a\u7528\u8ba1\u7b97\u65b9\u6cd5<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<pre><code class=\"language-katex\">\\left |\n\\begin{array}{l}\na_{11}&amp;a_{12}\\\\\na_{21}&amp;a_{22}\n\\end{array}\n\\right |=\na_{11}a_{22}-a_{12}a_{21}<\/code><\/pre>\n<h2><span class=\"ez-toc-section\" id=\"%E4%B8%89%E9%98%B6%E8%A1%8C%E5%88%97%E5%BC%8F%E9%80%9A%E7%94%A8%E8%AE%A1%E7%AE%97%E6%96%B9%E6%B3%95\"><\/span>\u4e09\u9636\u884c\u5217\u5f0f\u901a\u7528\u8ba1\u7b97\u65b9\u6cd5<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<pre><code class=\"language-katex\">\\left |\n\\begin{array}{l}\na_{11}&amp;a_{12}&amp;a_{13}\\\\\na_{21}&amp;a_{22}&amp;a_{23}\\\\\na_{31}&amp;a_{32}&amp;a_{33}\n\\end{array}\n\\right |=\na_{11}a_{22}a_{33}+a_{21}a_{32}a_{13}+a_{12}a_{23}a_{31}-a_{13}a_{22}a_{31}-a_{12}a_{21}a_{33}-a_{23}a_{32}a_{11}<\/code><\/pre>\n<p><img decoding=\"async\" data-src=\"https:\/\/blog.iyatt.com\/wp-content\/uploads\/2025\/08\/image-1755790083883.png\" alt=\"file\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" class=\"lazyload\" style=\"--smush-placeholder-width: 162px; --smush-placeholder-aspect-ratio: 162\/94;\" \/><br \/>\n\u4e4b\u79ef+<br \/>\n<img decoding=\"async\" data-src=\"https:\/\/blog.iyatt.com\/wp-content\/uploads\/2025\/08\/image-1755790103224.png\" alt=\"file\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" class=\"lazyload\" style=\"--smush-placeholder-width: 162px; --smush-placeholder-aspect-ratio: 162\/94;\" \/><br \/>\n\u4e4b\u79ef+<br \/>\n<img decoding=\"async\" data-src=\"https:\/\/blog.iyatt.com\/wp-content\/uploads\/2025\/08\/image-1755790117637.png\" alt=\"file\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" class=\"lazyload\" style=\"--smush-placeholder-width: 162px; --smush-placeholder-aspect-ratio: 162\/94;\" \/><br \/>\n\u4e4b\u79ef-<br \/>\n<img decoding=\"async\" data-src=\"https:\/\/blog.iyatt.com\/wp-content\/uploads\/2025\/08\/image-1755790148803.png\" alt=\"file\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" class=\"lazyload\" style=\"--smush-placeholder-width: 162px; --smush-placeholder-aspect-ratio: 162\/94;\" \/><br \/>\n\u4e4b\u79ef-<br \/>\n<img decoding=\"async\" data-src=\"https:\/\/blog.iyatt.com\/wp-content\/uploads\/2025\/08\/image-1755790175214.png\" alt=\"file\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" class=\"lazyload\" style=\"--smush-placeholder-width: 162px; --smush-placeholder-aspect-ratio: 162\/94;\" \/><br \/>\n\u4e4b\u79ef-<br \/>\n<img decoding=\"async\" data-src=\"https:\/\/blog.iyatt.com\/wp-content\/uploads\/2025\/08\/image-1755790190489.png\" alt=\"file\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" class=\"lazyload\" style=\"--smush-placeholder-width: 162px; --smush-placeholder-aspect-ratio: 162\/94;\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E5%AF%B9%E8%A7%92%E3%80%81%E4%B8%8A%EF%BC%88%E4%B8%8B%EF%BC%89%E4%B8%89%E8%A7%92%E8%A1%8C%E5%88%97%E5%BC%8F%E8%AE%A1%E7%AE%97%E6%96%B9%E6%B3%95\"><\/span>\u5bf9\u89d2\u3001\u4e0a\uff08\u4e0b\uff09\u4e09\u89d2\u884c\u5217\u5f0f\u8ba1\u7b97\u65b9\u6cd5<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e3b\u5bf9\u89d2\u7ebf<\/p>\n<pre><code class=\"language-katex\">\\left |\n\\begin{array}{l}\na_{11}&amp;0&amp;0&amp;0\\\\\n0&amp;a_{22}&amp;0&amp;0\\\\\n\\vdots&amp;\\vdots&amp;&amp;\\vdots\\\\\n0&amp;0&amp;\\cdots&amp;a_{nn}\n\\end{array}\n\\right|\n=\n\\left |\n\\begin{array}{l}\na_{11}&amp;a_{12}&amp;a_{13}&amp;a_{14}\\\\\n0&amp;a_{22}&amp;a_{23}&amp;a_{24}\\\\\n\\vdots&amp;\\vdots&amp;&amp;\\vdots\\\\\n0&amp;0&amp;\\cdots&amp;a_{nn}\n\\end{array}\n\\right|\n=\n\\left |\n\\begin{array}{l}\na_{11}&amp;0&amp;0&amp;0\\\\\na_{21}&amp;a_{22}&amp;0&amp;0\\\\\n\\vdots&amp;\\vdots&amp;&amp;\\vdots\\\\\na_{n1}&amp;a_{n2}&amp;\\cdots&amp;a_{nn}\n\\end{array}\n\\right|\n=\na_{11}a_{22}\\cdots a_{nn}<\/code><\/pre>\n<p>\u526f\u5bf9\u89d2\u7ebf<\/p>\n<pre><code class=\"language-katex\">\\left |\n\\begin{array}{l}\n0&amp;\\cdots&amp;0&amp;l_1\\\\\n0&amp;\\cdots&amp;l_2&amp;0\\\\\n\\vdots&amp;&amp;\\vdots&amp;\\vdots\\\\\nl_n&amp;\\cdots&amp;0&amp;0\n\\end{array}\n\\right|\n=\n\\left |\n\\begin{array}{l}\n0&amp;\\cdots&amp;0&amp;l_1\\\\\n0&amp;\\cdots&amp;l_2&amp;a_j\\\\\n\\vdots&amp;&amp;\\vdots&amp;\\vdots\\\\\nl_n&amp;\\cdots&amp;a_m&amp;a_k\n\\end{array}\n\\right|\n=\n\\left |\n\\begin{array}{l}\na_j&amp;\\cdots&amp;a_m&amp;l_1\\\\\na_k&amp;\\cdots&amp;l_2&amp;0\\\\\n\\vdots&amp;&amp;\\vdots&amp;\\vdots\\\\\nl_n&amp;\\cdots&amp;0&amp;0\n\\end{array}\n\\right|\n=\n(-1)^\\frac{n(n-1)}{2}l_1l_2\\cdots k_n<\/code><\/pre>\n<h2><span class=\"ez-toc-section\" id=\"%E8%8C%83%E5%BE%B7%E8%92%99%E8%A1%8C%E5%88%97%E5%BC%8F%E8%AE%A1%E7%AE%97\"><\/span>\u8303\u5fb7\u8499\u884c\u5217\u5f0f\u8ba1\u7b97<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<pre><code class=\"language-katex\">V(a_1,a_2,\\cdots,a_n)=\n\\left |\n\\begin{array}{l}\n1&amp;1&amp;\\cdots&amp;1\\\\\na_1&amp;a_2&amp;\\cdots&amp;a_n\\\\\n\\vdots&amp;\\vdots&amp;&amp;\\vdots\\\\\na_1^{n-1}&amp;a_2^{n-2}&amp;\\cdots&amp;a_n^{n-1}\n\\end{array}\n\\right |=\n\\prod_{1\\le j\\lt i\\le n}(a_i-a_j)<\/code><\/pre>\n<p><strong>\u4f8b:<\/strong><\/p>\n<pre><code class=\"language-katex\">\\begin{aligned}\n\\begin{vmatrix}\n1&amp;1&amp;1\\\\\n2&amp;1&amp;-3\\\\\n4&amp;1&amp;9\n\\end{vmatrix}&amp;=\n\n\\begin{vmatrix}\n1&amp;1&amp;1\\\\\n2^1&amp;1^1&amp;(-3)^1\\\\\n2^2&amp;1^2&amp;(-3)^2\n\\end{vmatrix}\\\\\n&amp;=\n(1-2)(-3-2)(-3-1)\\\\\n&amp;=\n-20\n\n\\end{aligned}<\/code><\/pre>\n<h2><span class=\"ez-toc-section\" id=\"%E5%88%86%E5%9D%97%E8%A1%8C%E5%88%97%E5%BC%8F\"><\/span>\u5206\u5757\u884c\u5217\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<pre><code class=\"language-katex\">\\begin{array}{l}\n\\begin{vmatrix}\nA_1&amp;&amp;&amp;\\\\\n&amp;A_2&amp;&amp;\\\\\n&amp;&amp;\\ddots&amp;\\\\\n&amp;&amp;&amp;A_n\n\\end{vmatrix}=\n|A_1|\\cdot|A_2|\\cdot\\cdots\\cdot|A_n|\\\\ \\\\\n\\begin{vmatrix}\nA&amp;C\\\\\nO&amp;B\n\\end{vmatrix}\n=\n\\begin{vmatrix}\nA&amp;O\\\\\nD&amp;B\n\\end{vmatrix}\n=|A|\\cdot|B|\\\\ \\\\\n\n\u8bbe A\uff0cB \u5206\u522b\u4e3a m\uff0cn \u9636\u77e9\u9635\uff0c\u5219\n\\begin{vmatrix}\nO&amp;A\\\\\nB&amp;O\n\\end{vmatrix}\n=\n(-1)^{mn}|A|\\cdot|B|\n\\end{array}<\/code><\/pre>\n<h2><span class=\"ez-toc-section\" id=\"%E8%A1%8C%E5%88%97%E5%BC%8F%E5%8F%98%E6%8D%A2%E6%80%A7%E8%B4%A8\"><\/span>\u884c\u5217\u5f0f\u53d8\u6362\u6027\u8d28<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>1.\u884c\u5217\u5f0f D \u4e0e\u5176\u8f6c\u7f6e\u884c\u5217\u5f0f <code class=\"katex-inline\">D^T<\/code>\u76f8\u7b49\u3002\u5373 <code class=\"katex-inline\">D=D^T<\/code>\uff1b<br \/>\n2.\u884c\u5217\u5f0f\u4efb\u610f\u4e24\u884c\uff08\u6216\u5217\uff09\u5bf9\u6362\uff0c\u6539\u53d8\u7b26\u53f7\u3002\u5982<code class=\"katex-inline\">\\begin{vmatrix}a_1&a_2\\\\a_3&a_4\\end{vmatrix}=-\\begin{vmatrix}a_2&a_1\\\\a_4&a_3\\end{vmatrix}<\/code><br \/>\n3.\u884c\u5217\u5f0f\u67d0\u884c\uff08\u6216\u5217\uff09\u6709\u516c\u56e0\u5b50\uff0c\u53ef\u4ee5\u63d0\u53d6\u5230\u884c\u5217\u5f0f\u5916\u9762\u3002\u5982<code class=\"katex-inline\">\\begin{vmatrix}5a_1&5a_2\\\\a_3&a_4\\end{vmatrix}=5\\begin{vmatrix}a_1&a_2\\\\a_3&a_4\\end{vmatrix}<\/code><br \/>\n3.1\u884c\u5217\u5f0f\u67d0\u884c\uff08\u6216\u5217\uff09\u5143\u7d20\u5168\u4e3a0\uff0c\u5219\u8be5\u884c\u5217\u5f0f\u4e3a0\u3002r\u5982<code class=\"katex-inline\">\\begin{vmatrix}a_1&a_2\\\\0&0\\end{vmatrix}=0<\/code><br \/>\n3.2\u884c\u5217\u5f0f\u67d0\u4e24\u884c\uff08\u6216\u5217\uff09\u5143\u7d20\u76f8\u540c\uff0c\u5219\u8be5\u884c\u5217\u5f0f\u4e3a0\u3002\u5982<code class=\"katex-inline\">\\begin{vmatrix}a_1&a_2\\\\a_1&a_2\\end{vmatrix}=0<\/code><br \/>\n3.3\u884c\u5217\u5f0f\u67d0\u4e24\u884c\uff08\u6216\u5217\uff09\u5143\u7d20\u5bf9\u5e94\u6210\u6bd4\u4f8b\uff0c\u5219\u884c\u5217\u5f0f\u4e3a0\u3002<code class=\"katex-inline\">\\begin{vmatrix}5a_1&5a_2\\\\a_1&a_2\\end{vmatrix}=0<\/code><br \/>\n4.\u884c\u5217\u5f0f\u67d0\u884c\uff08\u6216\u5217\uff09\u7684\u6bcf\u4e2a\u5143\u7d20\u90fd\u662f\u4e24\u6570\u4e4b\u548c\uff0c\u884c\u5217\u5f0f\u53ef\u5206\u89e3\u4e3a\u4e24\u4e2a\u884c\u5217\u5f0f\u4e4b\u548c\u3002\u5373<code class=\"katex-inline\">\\begin{vmatrix}a_{11}&a_{12}&\\cdots&a_{1n}\\\\ \\vdots&\\vdots&&\\vdots\\\\ a_{i1}+b_{i1}&a_{i2}+b_{i2}&\\cdots&a_{in}+b_{in}\\\\ \\vdots&\\vdots&& \\vdots\\\\ a_{n1}&a_{n2}&\\cdots&a_{nn}\\end{vmatrix}=\\begin{vmatrix}a_{11}&a_{12}&\\cdots&a_{1n}\\\\ \\vdots&\\vdots&&\\vdots\\\\ a_{i1}&a_{i2}&\\cdots&a_{in}\\\\ \\vdots&\\vdots&& \\vdots\\\\ a_{n1}&a_{n2}&\\cdots&a_{nn}\\end{vmatrix}+\\begin{vmatrix}a_{11}&a_{12}&\\cdots&a_{1n}\\\\ \\vdots&\\vdots&&\\vdots\\\\ b_{i1}&b_{i2}&\\cdots&b_{in}\\\\ \\vdots&\\vdots&& \\vdots\\\\ a_{n1}&a_{n2}&\\cdots&a_{nn}\\end{vmatrix}<\/code><br \/>\n5.\u884c\u5217\u5f0f\u7684\u67d0\u884c\uff08\u6216\u5217\uff09\u7684\u4efb\u610f\u500d\u6570\u52a0\u5230\u53e6\u5916\u4e00\u884c\uff08\u6216\u5217\uff09\uff0c\u884c\u5217\u5f0f\u503c\u4e0d\u53d8\u3002\u5982<code class=\"katex-inline\">\\begin{vmatrix}a_1&a_2\\\\a_3&a_4\\end{vmatrix}=\\begin{vmatrix}a_1&a_2\\\\a_3+3a_1&a_4+3a_2\\end{vmatrix}<\/code><\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E8%A1%8C%E5%88%97%E5%BC%8F%E9%99%8D%E9%98%B6%E6%80%A7%E8%B4%A8\"><\/span>\u884c\u5217\u5f0f\u964d\u9636\u6027\u8d28<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>1.\u884c\u5217\u5f0f\u7b49\u4e8e\u884c\u5217\u5f0f\u67d0\u884c\uff08\u6216\u5217\uff09\u5143\u7d20\u4e0e\u5176\u5bf9\u5e94\u7684\u4ee3\u6570\u4f59\u5b50\u5f0f\u4e4b\u79ef\u7684\u548c\uff0c\u5373<code class=\"katex-inline\">D=a_{i1}A_{i1}+a_{i2}A_{i2}+\\cdots+a_{in}A_{in}\uff08i=1,2,\\cdots,n\uff09<\/code>\u6216<code class=\"katex-inline\">D=a_{1j}A_{1j}+a_{2j}A_{2j}+\\cdots+a_{nj}A_{nj}\uff08j=1,2,\\cdots,n\uff09<\/code>\u3002\u5982<code class=\"katex-inline\">\\begin{vmatrix}1&2&3&4\\\\5&6&7&8\\\\9&10&11&12\\\\13&14&15&16\\end{vmatrix}=1\\times(-1)^{1+1}\\begin{vmatrix}6&7&8\\\\10&11&12\\\\14&15&16\\end{vmatrix}+2\\times(-1)^{1+2}\\begin{vmatrix}5&7&8\\\\9&11&12\\\\13&15&16\\end{vmatrix}+3\\times(-1)^{1+3}\\begin{vmatrix}5&6&8\\\\9&10&12\\\\13&14&16\\end{vmatrix}+4\\times(-1)^{1+4}\\begin{vmatrix}5&6&7\\\\9&10&11\\\\13&14&15\\end{vmatrix}<\/code><br \/>\n2.\u884c\u5217\u5f0f\u67d0\u884c\uff08\u6216\u5217\uff09\u7684\u5143\u7d20\u4e0e\u53e6\u5916\u4e00\u884c\uff08\u6216\u5217\uff09\u5bf9\u5e94\u5143\u7d20\u7684\u4ee3\u6570\u4f59\u5b50\u5f0f\u4e4b\u79ef\u7684\u548c\u4e3a0\uff0c\u5373<code class=\"katex-inline\">a_{i1}A_{j1}+a_{i2}A_{j2}+\\cdots+a_{in}A_{jn}=0\uff08i\\ne j\uff09<\/code>\u6216<code class=\"katex-inline\">a_{1i}A_{1j}+a_{2i}A_{2j}+\\cdots+a_{ni}A_{nj}=0\uff08i\\ne j\uff09<\/code><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6982\u5ff5 \u9006\u5e8f \u8bbe i\u3001j \u662f\u4e00\u5bf9\u4e0d\u7b49\u7684\u6b63\u6574\u6570\uff0c\u82e5 i &gt; j\uff0c\u5219\u79f0 (i, j) \u4e3a\u4e00\u5bf9\u9006\u5e8f\u3002 \u9006\u5e8f\u6570 \u4f8b [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"zakra_page_container_layout":"customizer","zakra_page_sidebar_layout":"customizer","zakra_remove_content_margin":false,"zakra_sidebar":"customizer","zakra_transparent_header":"customizer","zakra_logo":0,"zakra_main_header_style":"default","zakra_menu_item_color":"","zakra_menu_item_hover_color":"","zakra_menu_item_active_color":"","zakra_menu_active_style":"","zakra_page_header":true,"_lmt_disableupdate":"no","_lmt_disable":"no","footnotes":""},"categories":[1,612],"tags":[1627,1625,1624,1623,1629,1626,1628,1622,1619,1630,1620,1621],"class_list":["post-21497","post","type-post","status-publish","format-standard","hentry","category-all","category-612","tag-1627","tag-1625","tag-1624","tag-1623","tag-1629","tag-1626","tag-1628","tag-1622","tag-1619","tag-1630","tag-1620","tag-1621"],"modified_by":"IYATT-yx","_links":{"self":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts\/21497","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=21497"}],"version-history":[{"count":18,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts\/21497\/revisions"}],"predecessor-version":[{"id":21865,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts\/21497\/revisions\/21865"}],"wp:attachment":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=21497"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=21497"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=21497"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}