{"id":443,"date":"2021-05-08T22:04:06","date_gmt":"2021-05-08T14:04:06","guid":{"rendered":"http:\/\/www.wayln.com\/?p=443"},"modified":"2021-05-08T22:13:30","modified_gmt":"2021-05-08T14:13:30","slug":"4-6-%e7%a7%a9","status":"publish","type":"post","link":"http:\/\/www.wayln.com\/?p=443","title":{"rendered":"4.6 \u79e9"},"content":{"rendered":"<div id=\"toc_container\" class=\"toc_transparent no_bullets\"><p class=\"toc_title\">Contents<\/p><ul class=\"toc_list\"><li><a href=\"#i\"><span class=\"toc_number toc_depth_1\">1<\/span> \u884c\u7a7a\u95f4<\/a><\/li><li><a href=\"#i-2\"><span class=\"toc_number toc_depth_1\">2<\/span> \u79e9\u5b9a\u7406<\/a><\/li><li><a href=\"#i-3\"><span class=\"toc_number toc_depth_1\">3<\/span> \u79e9\u548c\u53ef\u9006\u77e9\u9635\u5b9a\u7406<\/a><\/li><\/ul><\/div>\n<h1><span id=\"i\">\u884c\u7a7a\u95f4<\/span><\/h1>\n<p>\u82e5A\u662f\u4e00\u4e2amxn\u77e9\u9635\uff0cA\u7684\u6bcf\u4e00\u884c\u5177\u6709n\u4e2a\u6570\u5b57\uff0c\u5373\u53ef\u4ee5\u89c6\u4e3a<span class=\"katex math inline\">R^n<\/span>\u4e2d\u4e00\u4e2a\u5411\u91cf\u3002\u5176\u884c\u5411\u91cf\u7684\u6240\u6709\u7ebf\u6027\u7ec4\u5408\u7684\u96c6\u5408\u79f0\u4e3aA\u7684<strong>\u884c\u7a7a\u95f4<\/strong>\uff0c\u8bb0\u4e3aRow A\u3002\u7531\u4e8e\u6bcf\u4e00\u884c\u5177\u6709n\u4e2a\u6570\uff0c\u6240\u4ee5Row A\u662f<span class=\"katex math inline\">R^n<\/span>\u7684\u4e00\u4e2a\u5b50\u7a7a\u95f4\uff0c\u56e0\u4e3aA\u7684\u884c\u4e0e<span class=\"katex math inline\">A^T<\/span>\u7684\u5217\u76f8\u540c\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u7528<span class=\"katex math inline\">ColA^T<\/span>\u4ee3\u66ffRow A\u3002<\/p>\n<blockquote><p>\n  <strong>\u5b9a\u740613<\/strong>\u3000\u82e5\u4e24\u4e2a\u77e9\u9635A\u548cB\u884c\u7b49\u4ef7\uff0c\u5219\u4ed6\u4eec\u7684\u884c\u7a7a\u95f4\u76f8\u540c\u3002\u82e5B\u662f\u9636\u68af\u578b\u77e9\u9635\uff0c\u5219B\u7684\u975e\u96f6\u884c\u6784\u6210A\u7684\u884c\u7a7a\u95f4\u7684\u4e00\u4e2a\u57fa\u7684\u540c\u4e8b\u4e5f\u662fB\u7684\u884c\u7a7a\u95f4\u7684\u4e00\u4e2a\u57fa\n<\/p><\/blockquote>\n<p><strong>\u4f8b2<\/strong>\u3000\u5206\u522b\u6c42\u77e9\u9635A\u7684\u884c\u7a7a\u95f4\u3001\u5217\u7a7a\u95f4\u548c\u96f6\u7a7a\u95f4\u7684\u57fa\u3002<\/p>\n<div class=\"katex math multi-line no-emojify\">A=\\left[\\begin{array}{rrrrr}<br \/>\n-2&amp;-5&amp;8&amp;0&amp;-7\\\\<br \/>\n1&amp;3&amp;-5&amp;1&amp;5\\\\<br \/>\n3&amp;11&amp;-19&amp;7&amp;1\\\\<br \/>\n1&amp;7&amp;-13&amp;5&amp;-3\\\\<br \/>\n\\end{array}\\right]\n<\/div>\n<p>\u89e3 \u4e3a\u4e86\u6c42\u884c\u7a7a\u95f4\u548c\u5217\u7a7a\u95f4\u7684\u57fa\uff0c\u884c\u5316\u7b80A\u6210\u9636\u68af\u5f62\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">A \\sim B=\\left[\\begin{array}{rrrrr}<br \/>\n1&amp;3&amp;-5&amp;1&amp;5\\\\<br \/>\n0&amp;1&amp;-2&amp;2&amp;-7\\\\<br \/>\n0&amp;0&amp;0&amp;-4&amp;20\\\\<br \/>\n0&amp;0&amp;0&amp;0&amp;0\\\\<br \/>\n\\end{array}\\right]\n<\/div>\n<p>\u6709\u5b9a\u740613\uff0cB\u7684\u524d\u4e09\u884c\u6784\u6210A\u7684\u884c\u7a7a\u95f4\u7684\u4e00\u4e2a\u57fa\uff08\u4e5f\u662fB\u7684\u884c\u7a7a\u95f4\u7684\u57fa\uff09\uff0c\u4ece\u800c<\/p>\n<div class=\"katex math multi-line no-emojify\">Row A\u7684\u57fa\uff1a\\{(1,3,-5,1,5),(0,1,-2,2,-7),(0,0,0,-4,20)\\}\n<\/div>\n<p>\u5bf9\u5217\u7a7a\u95f4\uff0c\u89c2\u5bdfB\uff0c\u4f4f\u9662\u5217\u5728\u7b2c1,2\u548c4\u5217\uff0c\u4ece\u800cA\u7684\u7b2c1,2,4\u5217\uff08\u4e0d\u662fB\u7684\uff09\u6784\u6210ColA\u7684\u4e00\u4e2a\u57fa\u3002<\/p>\n<div class=\"katex math multi-line no-emojify\">Col A\u7684\u57fa\uff1a\\left[\\begin{array}{r}-2\\\\1\\\\3\\\\1\\end{array}\\right],<br \/>\n\\left[\\begin{array}{r}-5\\\\3\\\\11\\\\7\\end{array}\\right],<br \/>\n\\left[\\begin{array}{r}0\\\\1\\\\7\\\\5\\end{array}\\right]\n<\/div>\n<p>\u6ce8\u610f\u5230A\u7684\u4efb\u4f55\u9636\u68af\u5f62\u63d0\u4f9b\uff08\u5728\u5b83\u7684\u975e\u96f6\u884c\uff09Row A\u7684\u4e00\u4e2a\u57fa\u540c\u65f6\u5bf9Col A\u786e\u5b9a\u4e86A\u7684\u4e3b\u5143\u5217\u3002<br \/>\n\u7136\u800c\u5bf9Nul A,\u5219\u9700\u8981\u7b80\u5316\u9636\u68af\u5f62\uff0c\u5219B\u8fdb\u4e00\u6b65\u884c\u53d8\u6362\u7684\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">A \\sim B \\sim C=\\left[\\begin{array}{rrrrr}<br \/>\n1&amp;0&amp;1&amp;0&amp;1\\\\<br \/>\n0&amp;1&amp;-2&amp;0&amp;3\\\\<br \/>\n0&amp;0&amp;0&amp;1&amp;-5\\\\<br \/>\n0&amp;0&amp;0&amp;0&amp;0\\\\<br \/>\n\\end{array}\\right]\n<\/div>\n<p>\u65b9\u7a0b<span class=\"katex math inline\">Ax=0<\/span>\u7b49\u4ef7\u4e8eCx=0,\u5373<\/p>\n<div class=\"katex math multi-line no-emojify\">\\begin{cases}<br \/>\nx_1+x_3+x_5=0\\\\<br \/>\nx_2-2x_3+3x_5=0\\\\<br \/>\nx_4-5x_5=0<br \/>\n\\end{cases}\n<\/div>\n<p>\u6240\u4ee5<span class=\"katex math inline\">x_1=-x_3-x_5,x_2=2x_3-3x_5,x_4=5x_5,x_3\u548cx_5<\/span>\u4e3a\u81ea\u7531\u53d8\u91cf\uff0c\u901a\u5e38\u7684\u8ba1\u7b97\u8868\u660e\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">Nul A\u7684\u57fa\uff1a\\left[\\begin{array}{r}-1\\\\2\\\\1\\\\0\\\\0\\end{array}\\right],<br \/>\n\\left[\\begin{array}{r}-1\\\\-3\\\\0\\\\5\\\\1\\end{array}\\right]\n<\/div>\n<p>\u901a\u8fc7\u89c2\u5bdf\u8bfe\u4ef6\uff0c\u4e0eCol A\u7684\u57fa\u4e0d\u540c\uff0cRow A\u548cNul A\u7684\u57fa\u4e8eA\u4e2d\u7684\u6570\u6ca1\u6709\u7b80\u5355\u7684\u8054\u7cfb\u3002<\/p>\n<div class=\"katex math multi-line no-emojify\">{\\color{red} **\u8b66\u544a**\u3000\u5728\u4f8b2\u4e2d\uff0c\u5c3d\u7ba1B\u7684\u524d\u4e09\u884c\u662f\u7ebf\u6027\u65e0\u5173\u7684\uff0c\u4f46\u7531\u6b64\u63a8\u65ad\u8bf4A\u7684\u524d\u4e09\u884c\u662f\u7ebf\u6027\u65e0\u5173\u5219\u662f\u9519\u8bef\u7684\uff08\u4e8b\u5b9e\u4e0aA\u7684\u7b2c\u4e09\u884c\u7b49\u4e8e2\u500d\u7684\u7b2c\u4e00\u884c\u52a0\u4e0a7\u500d\u7684\u7b2c\u4e8c\u884c\uff09\uff0c\u884c\u53d8\u6362\u5bf9\u77e9\u9635\u7684\u884c\u4e0d\u4fdd\u6301\u7ebf\u6027\u76f8\u5173\u5173\u7cfb}\n<\/div>\n<h1><span id=\"i-2\">\u79e9\u5b9a\u7406<\/span><\/h1>\n<blockquote><p>\n  <strong>\u5b9a\u4e49<\/strong>\u3000A\u7684\u79e9\u5373A\u7684\u5217\u7a7a\u95f4\u7684\u7ef4\u6570\n<\/p><\/blockquote>\n<p>\u7531\u4e8e<span class=\"katex math inline\">Row A<\/span>\u4e0e <span class=\"katex math inline\">ColA^T<\/span>\u76f8\u540c\uff0c\u5219A\u7684\u884c\u7a7a\u95f4\u7684\u7ef4\u6570\u7b49\u4e8e<span class=\"katex math inline\">A^T<\/span>\u7684\u79e9\uff0c\u96f6\u7a7a\u95f4\u7684\u7ef4\u6570\u6709\u65f6\u88ab\u79f0\u4e3aA\u7684\u96f6\u7ef4\u3002<\/p>\n<blockquote><p>\n  <strong>\u5b9a\u740614<\/strong> \uff08\u79e9\u5b9a\u7406\uff09<br \/>\n  mxn\u77e9\u9635A\u7684\u5217\u7a7a\u95f4\u548c\u884c\u7a7a\u95f4\u7684\u7ef4\u6570\u76f8\u7b49\uff0c\u8fd9\u4e2a\u516c\u5171\u7684\u7ef4\u6570(\u5373A\u7684\u79e9)\u8fd8\u7b49\u4e8eA\u7684\u4e3b\u5143\u4f4d\u7f6e\u7684\u4e2a\u6570\u4e14\u6ee1\u8db3\u65b9\u7a0b\n<\/p><\/blockquote>\n<div class=\"katex math multi-line no-emojify\">rank A+\\dim NulA=n\n<\/div>\n<h1><span id=\"i-3\">\u79e9\u548c\u53ef\u9006\u77e9\u9635\u5b9a\u7406<\/span><\/h1>\n<blockquote><p>\n  <strong>\u5b9a\u7406<\/strong>\u3000(\u53ef\u9006\u77e9\u9635\u5b9a\u7406(\u7eed))<br \/>\n  \u4ee4A\u662f\u4e00\u4e2anxn\u77e9\u9635\uff0c\u5219\u4e0b\u5217\u7684\u547d\u9898\u4e2d\u7684\u6bcf\u4e2a\u5747\u7b49\u4ef7\u4e8eA\u662f\u53ef\u9006\u77e9\u9635\uff1a<br \/>\n  m.\u3000A\u7684\u5217\u6784\u6210<span class=\"katex math inline\">R^n<\/span>\u7684\u4e00\u4e2a\u57fa<br \/>\n  n.\u3000ColA=<span class=\"katex math inline\">R^n<\/span><br \/>\n  o.\u3000<span class=\"katex math inline\">\\dim ColA=n<\/span><br \/>\n  p.\u3000<span class=\"katex math inline\">rankA=n<\/span><br \/>\n  q.\u3000<span class=\"katex math inline\">Nul A=&#92;{0&#92;}<\/span><br \/>\n  r.\u3000<span class=\"katex math inline\">\\dim NulA=0<\/span>\n<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>Contents1 \u884c\u7a7a\u95f42 \u79e9\u5b9a\u74063 \u79e9\u548c\u53ef\u9006\u77e9\u9635\u5b9a\u7406 \u884c\u7a7a\u95f4 \u82e5A\u662f\u4e00\u4e2amxn\u77e9\u9635\uff0cA\u7684\u6bcf\u4e00\u884c\u5177\u6709n\u4e2a\u6570\u5b57 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":342,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21,22,26],"tags":[],"class_list":["post-443","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\/443","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=443"}],"version-history":[{"count":3,"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/443\/revisions"}],"predecessor-version":[{"id":446,"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/443\/revisions\/446"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/media\/342"}],"wp:attachment":[{"href":"http:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=443"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=443"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=443"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}