{"id":21958,"date":"2025-10-02T20:19:03","date_gmt":"2025-10-02T12:19:03","guid":{"rendered":"https:\/\/blog.iyatt.com\/?p=21958"},"modified":"2025-10-02T20:19:18","modified_gmt":"2025-10-02T12:19:18","slug":"%e6%9c%89%e9%99%90%e6%ac%a1%e5%88%9d%e7%ad%89%e5%8f%98%e6%8d%a2%e6%b1%82%e8%a7%a3%e7%9f%a9%e9%98%b5%e6%96%b9%e7%a8%8b","status":"publish","type":"post","link":"https:\/\/blog.iyatt.com\/?p=21958","title":{"rendered":"\u6709\u9650\u6b21\u521d\u7b49\u53d8\u6362\u6c42\u89e3\u77e9\u9635\u65b9\u7a0b"},"content":{"rendered":"<p>\u2460\u82e5\u6709<code class=\"katex-inline\">AX=B<\/code>\uff0c\u53ef\u4ee5\u5c06A\u548cB\u7ec4\u6210\u589e\u5e7f\u77e9\u9635<code class=\"katex-inline\">(A|B)<\/code>\uff0c\u8fdb\u884c\u6709\u9650\u6b21\u521d\u7b49\u884c\u53d8\u6362\uff0c\u4f7f\u7cfb\u6570\u77e9\u9635A\u7684\u4f4d\u7f6e\u53d8\u4e3a\u5355\u4f4d\u77e9\u9635E\uff0c\u5f97\u5230<code class=\"katex-inline\">(E|A^{-1}B)<\/code>\uff0c\u6b64\u65f6\u5e38\u6570\u77e9\u9635B\u7684\u4f4d\u7f6e\u5c31\u662f<code class=\"katex-inline\">A^{-1}B<\/code>\uff0c\u5373 X \u7684\u89e3\u3002<br \/>\n\u2461\u82e5\u6709<code class=\"katex-inline\">XA=B<\/code>\uff0c\u53ef\u4ee5\u5c06A\u548cB\u7ec4\u6210\u589e\u5e7f\u77e9\u9635<code class=\"katex-inline\">\\begin{pmatrix}A\\\\-\\\\B\\end{pmatrix}<\/code>\uff0c\u8fdb\u884c\u6709\u9650\u6b21\u521d\u7b49\u5217\u53d8\u6362\uff0c\u4f7f\u7cfb\u6570\u77e9\u9635A\u7684\u4f4d\u7f6e\u53d8\u4e3a\u5355\u4f4d\u77e9\u9635E\uff0c\u5f97\u5230<code class=\"katex-inline\">\\begin{pmatrix}E\\\\---\\\\A^{-1}B\\end{pmatrix}<\/code>\uff0c\u6b64\u65f6\u5e38\u6570\u77e9\u9635B\u7684\u4f4d\u7f6e\u5c31\u662f<code class=\"katex-inline\">BA^{-1}<\/code>\uff0c\u5373 X \u7684\u89e3\u3002<\/p>\n<p>\u4f8b\uff1a<code class=\"katex-inline\">\\begin{pmatrix}1&4\\\\-1&2\\end{pmatrix}X\\begin{pmatrix}2&0\\\\-1&1\\end{pmatrix}=\\begin{pmatrix}3&1\\\\0&-1\\end{pmatrix}<\/code>\uff0c\u6c42 X<\/p>\n<pre><code class=\"language-katex\">\\begin{array}{l}\n\u4ee4A=\\begin{pmatrix}1&amp;4\\\\-1&amp;2\\end{pmatrix}\uff0c\nB=\\begin{pmatrix}2&amp;0\\\\-1&amp;1\\end{pmatrix}\uff0c\nC=\\begin{pmatrix}3&amp;1\\\\0&amp;-1\\end{pmatrix} \\\\\n\u77e9\u9635\u65b9\u7a0b\u53ef\u4ee5\u8868\u793a\u4e3aAXB=C\\\\\n\u2460\u5148\u6c42XB\uff0cXB=A^{-1}C \\\\\n\uff08A|C)=\\begin{pmatrix}1&amp;4&amp;|&amp;3&amp;1\\\\-1&amp;2&amp;|&amp;-1&amp;1\\end{pmatrix}\\rightarrow\n\\begin{pmatrix}1&amp;0&amp;|&amp;1&amp;1\\\\0&amp;1&amp;|&amp;\\frac12&amp;0\\end{pmatrix}=(E|A^{-1}C)\\\\\n\u5373A^{-1}C=\\begin{pmatrix}1&amp;1\\\\\\frac12&amp;0\\end{pmatrix}\\\\\n\u2461\u518d\u6c42X\uff0cX=A^{-1}CB^{-1}\\\\\n\\begin{pmatrix}B\\\\---\\\\A^{-1}C\\end{pmatrix}=\n\\begin{pmatrix}2&amp;0\\\\-1&amp;1\\\\-&amp;-\\\\1&amp;1\\\\\\frac12&amp;0\\end{pmatrix}\\rightarrow\n\\begin{pmatrix}1&amp;0\\\\0&amp;1\\\\-&amp;-\\\\1&amp;1\\\\\\frac14&amp;0\\end{pmatrix}\n=\\begin{pmatrix}E\\\\---\\\\A^{-1}CB^{-1}\\end{pmatrix}\\\\\n\u5373X=A^{-1}CB^{-1}=\\begin{pmatrix}1&amp;1\\\\\\frac14&amp;0\\end{pmatrix}\n\\end{array}<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"<p>\u2460\u82e5\u6709AX=B\uff0c\u53ef\u4ee5\u5c06A\u548cB\u7ec4\u6210\u589e\u5e7f\u77e9\u9635(A|B)\uff0c\u8fdb\u884c\u6709\u9650\u6b21\u521d\u7b49\u884c\u53d8\u6362\uff0c\u4f7f\u7cfb\u6570\u77e9\u9635A\u7684\u4f4d\u7f6e\u53d8\u4e3a\u5355\u4f4d\u77e9\u9635E\uff0c\u5f97 [&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":[],"class_list":["post-21958","post","type-post","status-publish","format-standard","hentry","category-all","category-612"],"modified_by":"IYATT-yx","_links":{"self":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts\/21958","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=21958"}],"version-history":[{"count":1,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts\/21958\/revisions"}],"predecessor-version":[{"id":21959,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts\/21958\/revisions\/21959"}],"wp:attachment":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=21958"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=21958"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=21958"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}