{"id":325,"date":"2021-04-14T21:50:27","date_gmt":"2021-04-14T13:50:27","guid":{"rendered":"http:\/\/www.wayln.com\/?p=325"},"modified":"2021-04-15T10:49:26","modified_gmt":"2021-04-15T02:49:26","slug":"3-1%e8%a1%8c%e5%88%97%e5%bc%8f%e4%bb%8b%e7%bb%8d","status":"publish","type":"post","link":"http:\/\/www.wayln.com\/?p=325","title":{"rendered":"3.1\u884c\u5217\u5f0f\u4ecb\u7ecd"},"content":{"rendered":"<blockquote><p>\n  <strong>\u5b9a\u4e49<\/strong>\u3000\u5f53<span class=\"katex math inline\">n \\geq2,<\/span>nxn\u77e9\u9635<span class=\"katex math inline\">A=\\begin{bmatrix}a_{ij}\\end{bmatrix}<\/span>\u7684\u884c\u5217\u5f0f\u662f\u5f62\u5982<span class=\"katex math inline\">\\pm a_{1j}detA_{1j}<\/span>\u7684n\u4e2a\u9879\u7684\u548c\uff0c\u5176\u4e2d\u52a0\u53f7\u548c\u51cf\u53f7\u4ea4\u66ff\u51fa\u73b0\uff0c\u8fd9\u91cc\u5143\u7d20<span class=\"katex math inline\">a_{11},a_{12},\\dots,a_{1n}<\/span>\u6765\u81eaA\u7684\u7b2c\u4e00\u884c\uff0c\u5373<\/p>\n<div class=\"katex math multi-line no-emojify\">detA=a_12\\cdot detA_{11}-a_{12}\\cdot detA_{12}+\\dots+(-1)^{1+n}a_{1n}\\cdot &gt;detA_{1n}\n  <\/div>\n<div class=\"katex math multi-line no-emojify\">=\\sum_{j=1}^n(-1)^{1+j}a_{1j}detA_{1j}\n  <\/div>\n<\/blockquote>\n<p>\u4e3a\u4e86\u53d9\u8ff0\u4e0b\u4e00\u5b9a\u7406\uff0c\u5c06<span class=\"katex math inline\">detA<\/span>\u7684\u5b9a\u4e49\u7528\u7a0d\u5fae\u4e0d\u540c\u7684\u5f62\u52bf\u5199\u51fa\u8bd7\u5f88\u65b9\u4fbf\u7684\u3002\u7ed9\u5b9a<span class=\"katex math inline\">A=\\begin{bmatrix}a_{ij}\\end{bmatrix}<\/span>,A\u7684\uff08i,j\uff09<strong>\u4f59\u56e0\u5b50<\/strong>$C_{ij}$\u7531\u4e0b\u5f0f\u7ed9\u51fa<\/p>\n<div class=\"katex math multi-line no-emojify\">C_{ij}=(-1)^{i+j}detA_{ij} \\tag{4}\n<\/div>\n<p>\u5219<span class=\"katex math inline\">detA=a_{11}\\cdot C_{11}+a_{12}\\cdot C_{12}+\\dots+a_{1n}\\cdot C_{1n}<\/span><br \/>\n\u8fd9\u4e2a\u516c\u5f0f\u79f0\u4e3a\u6309A\u7684\u7b2c\u4e00\u884c\u7684\u4f59\u56e0\u5b50\u5c55\u5f00\u5f0f<\/p>\n<blockquote><p>\n  <em>\u5b9a\u74061<\/em> mxm\u77e9\u9635A\u7684\u884c\u5217\u5f0f\u53ef\u6309\u4efb\u610f\u884c\u6216\u5217\u7684\u4f59\u56e0\u5b50\u5c55\u5f00\u5f0f\u6765\u8ba1\u7b97\u3002\u6309\u7b2ci\u884c\u5c55\u5f00\u7528(4)\u5f0f\u7ed9\u51fa\u7684\u4f59\u56e0\u5b50\u5199\u6cd5\u53ef\u4ee5\u5199\u6210\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">detA=a_{i1}C_{i1}+a_{i2}C_{i2}+\\dots+a_{in}C_{in}\n  <\/div>\n<p>  \u6309\u7b2cJ\u5217\u7684\u4f59\u56e0\u5b50\u5c55\u5f00\u5f0f\u4e3a<\/p>\n<div class=\"katex math multi-line no-emojify\">detA=a_{1j}C_{1j}+a_{2j}C_{2j}+\\dots+a_{nj}C_{nj}\n  <\/div>\n<\/blockquote>\n<p>\uff08i,j\uff09\u4f4d\u7f6e\u7684\u4f59\u56e0\u5b50\u4e2d\u52a0\u53f7\u6216\u51cf\u53f7\u53d6\u51b3\u4e8e<span class=\"katex math inline\">a_{ij}<\/span>\u5728\u77e9\u9635\u4e2d\u7684\u4f4d\u7f6e\uff0c\u800c\u4e0e<span class=\"katex math inline\">a_{ij}<\/span>\u672c\u8eab\u7684\u7b26\u53f7\u65e0\u5173<\/p>\n<blockquote><p>\n  <strong>\u5b9a\u74062<\/strong> \u82e5<span class=\"katex math inline\">A<\/span>\u4e3a\u4e09\u89d2\u9635\uff0c\u5219<span class=\"katex math inline\">detA<\/span>\u7b49\u4e8e<span class=\"katex math inline\">A<\/span>\u7684\u4e3b\u5bf9\u89d2\u7ebf\u4e0a\u5143\u7d20\u7684\u4e58\u79ef\n<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>\u5b9a\u4e49\u3000\u5f53n \\geq2,nxn\u77e9\u9635A=\\begin{bmatrix}a_{ij}\\end{bmatrix}\u7684\u884c [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":331,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21,22,26],"tags":[],"class_list":["post-325","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-21","category-22","category-26"],"_links":{"self":[{"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/325","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=325"}],"version-history":[{"count":6,"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/325\/revisions"}],"predecessor-version":[{"id":346,"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/325\/revisions\/346"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/media\/331"}],"wp:attachment":[{"href":"http:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=325"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=325"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=325"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}