• 2022-06-07
    求下三角阵的逆矩阵的详细算法.[解]设下三角矩阵[tex=0.714x1.286]18M6ew5gR6NB86zTl6PXxg==[/tex]的逆矩阵为[tex=0.714x1.286]atrPPistVyxj7cY8rjePCQ==[/tex].[tex=11.5x5.357]vo48hbmLLEz9zaNnVYxUcfAjJgOvqpv8MAjAx6Oq6jRdYXA6p27a9GappMDn/xBz/JENK9f3Uqzv3jnYzxfqJo92QmR3IVjTaWyoptNMbUT5p6VaY9NmndXWP1pZSkEyi6XBAzdezMYS18q/0GDbPwdv7yyt0uVnNc8WUWY9+cj0wcML4mINDtEcXJVKwMhu9qbT6JRex+R2tVe1pN1zBg==[/tex],[tex=11.643x5.214]lpBwrVFLJYshQ4k3NHGzd05UFuigfXuavadlrAz6F/NhxeUaO85eP4RQA5zFFjH9WQiI7VR7MaSuGw2+Rmi/XxCEiCuqIjTf3yiyMXNvT14g86QvpvApBY22+Fm3JGO4cN1LB7Fryd3Arz6zIZKezpSsNs1iVK1xtvCERH8RYuYk1a8fKGTynM2naxENOQ1+RDOpRPpB3juFyQQbEoL/EQ==[/tex]我们可以使用待定法,求出矩阵[tex=0.714x1.286]atrPPistVyxj7cY8rjePCQ==[/tex]的各列向量.为此我们将[tex=0.714x1.286]atrPPistVyxj7cY8rjePCQ==[/tex]按列分块如下:[tex=8.214x1.286]lUJcX4Yj2g1FmkSKz4eBAH3tIQX721j3rN+BJgpnXtr3IeQRaXm5Ds5/9cl0LcNF[/tex],注意到:[tex=19.857x1.286]W6Bmp9S5DE9qYf4BwalGYpLGgtBxfpp4g66e+0e4wB6t9yLUaLK5ZSf4Jeohyr9EK6e/UXkxQUHNEYxxeqUMgxKZ/bhNxwbipyHj/guqXMtanhqsUzoO/BuKdnSoxJK81ADIKlEHgvmb+bfz9yJPCQ==[/tex],我们只需运用算法[tex=2.857x1.286]zTbg2qfvBskTzaIuXR/Z8WvW94eSGd+FHJ3vm8YWO+8=[/tex],逐一求解方程[tex=3.571x1.286]mh2HBd3tMzaIce0qtoWE5QR/CrISlfhX7imYlH8mKtg=[/tex],[tex=2.071x1.286]39Ksdnhe4VFbg5M7evRYtw==[/tex],[tex=0.5x1.286]AO16NTt3MKb6K8RJQb3PEw==[/tex],[tex=1.143x1.286]PZ3wc82RrbgX5KwVcyJcmA==[/tex],[tex=0.643x1.286]ZsZs11iKEvfmzDIurZth8g==[/tex],便可求得[tex=3.643x1.286]Jxc7Sr9GzjvEIfT4vWj7Gg==[/tex].
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