已知 [tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex] 阶方阵 [tex=2.0x1.214]vnzjVhyzo/NIhVUgFyjLlA==[/tex] 满足条件 [tex=4.143x1.0]4EGwtNPILOTkGljLrP4Ukw==[/tex] 求 [tex=5.5x2.786]jcCMHflCR8OS9TosV6N5vG1RhOgz37MfZIZv5lwsozfeNWs2Xtqnv6P48tdqQzwA/vJl2nCoz0qK3550AgQDVw==[/tex].

2022-07-25

已知 [tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex] 阶方阵 [tex=2.0x1.214]vnzjVhyzo/NIhVUgFyjLlA==[/tex] 满足条件 [tex=4.143x1.0]4EGwtNPILOTkGljLrP4Ukw==[/tex] 求 [tex=5.5x2.786]jcCMHflCR8OS9TosV6N5vG1RhOgz37MfZIZv5lwsozfeNWs2Xtqnv6P48tdqQzwA/vJl2nCoz0qK3550AgQDVw==[/tex].

答案：

解 所求矩阵为 [tex=3.643x1.357]JHQ6dsNVRVXigwT4GNztWQ==[/tex], 其中[p=align:center][tex=15.143x2.786]7cmsJbY6FPlCRCIcVTXj2tBnopUj8/AmmwjSyCCsffFyOiEHWSmGONgNbQcKR+IbbXOohRnUspTaqh5o6C93bEew3e6vprfsZqQPSq+Y4eVWAUEyg1PnX+D6xL6+7TV9ZF3PzztONvV++d+qXcAfIEXuNX+2y/FwSd666cB7a0U321d+3j3P74nO8wIhsAZc[/tex]由 [tex=3.857x1.0]ooePFz0xjtusf6vpqQWa8A==[/tex] 知 [tex=4.357x1.0]/pQO+sD8B2aRvYJtdRSOnw==[/tex] 因此可用牛顿二项式定理展开得[p=align:center][tex=20.5x2.429]1YmlFD6XDSnwReFasmDG/sREdi+OuzUW4zWsx0/Gk3AvbBMpyobDI6AG4yxDu3vP1JjLiN4RZuti99Fa8JKWgfrm3+m0sECY7ZKTlFtuHv4=[/tex]易验证 [tex=2.857x1.214]dmCs8xXtmd/jdDctA0klzg==[/tex], 因而 [tex=7.143x1.214]21gPsCUg3Fwkz3AX4eP7KnpK/zDFRYe7AleZlCwxQU4=[/tex] 对 [tex=2.357x1.143]RlirBdRhOxl1BC2ROj1aBA==[/tex] 成立. 因此得到所求矩阵为[tex=27.143x5.714]1YmlFD6XDSnwReFasmDG/p2RLnoQ/q2GKvyMt8M3Z1UyMGrKUusQe+g0sreQWKR2vDHCzCsEM9LCkQuaMAHBYnGph71lCtJdz5916wDwOAP2ot6u411XhE+aIQ/hQYMgp4hb+YCUf2Otjvl5row/HkP421F8WQdwoz/s03DX7fie+XVlPPrdyk2ZwhLIGynQ3WMXo1oiA1AMJ3bNIJJRHGK4t6pVoBCEgpvK9M3EkHB5HKSRjtpkxOuD/j9qQGBwndv823pHsMdJJGM6PMrgg/MpesW7FQ9gt6JHaoEVinxJQRehwSSu15tiOsGM2wnuEHJms4EHfKXRadZHxU+6Z4PQ5NDjnsn10MDh497cS68=[/tex]

举一反三

内容

0
设[tex=2.0x1.214]vnzjVhyzo/NIhVUgFyjLlA==[/tex]都是[tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex]阶矩阵，命题"若[tex=2.0x1.214]vnzjVhyzo/NIhVUgFyjLlA==[/tex]都可逆。则[tex=2.286x1.143]Px4s+PosevWooBpZPidJvg==[/tex]也可逆"是否成立?
1
设 [tex=2.0x1.214]vnzjVhyzo/NIhVUgFyjLlA==[/tex]均为 [tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex]阶可逆矩阵，证明: [tex=6.214x1.357]7fk4PDAIPUAv1IgmkEs0Sbf05bnZtcbLsuVNpoSi4Z3eOOK/Ve5LV7wwbbwUB+k0+VhoMpWp41AeaOBiM8sOhA==[/tex].
2
若 [tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex] 阶实方阵 [tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex] 满足 [tex=3.429x1.357]NW79iFfJTlsydH9/AAtyCKvH0wgzaYujcWhDbZkUghY=[/tex], 则称为正交矩阵. 证明: 不存在 [tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex] 阶正交矩阵 [tex=2.0x1.214]vnzjVhyzo/NIhVUgFyjLlA==[/tex] 满足 [tex=5.857x1.357]Qg1OcQHVXCik8ADiEtZwP8gM0TtvjvHOo32HB7nB3dM=[/tex], 其中 [tex=0.5x0.786]hycNLgozeED/VkKdun7zdA==[/tex] 是非零常数.
3
设 [tex=1.143x1.071]DFelGZAPNOqMgdbfKVoEHA==[/tex] 表示 [tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex] 阶方阵 [tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex] 的附属方阵. 证明: [tex=5.786x1.357]cRSSutUe8lxP7o+KrExJjIlQDv25D1qSOdQh99TznTk=[/tex] 对任意同阶方阵 [tex=2.0x1.214]vnzjVhyzo/NIhVUgFyjLlA==[/tex] 成立;[br][/br]
4
已知[tex=2.0x1.214]vnzjVhyzo/NIhVUgFyjLlA==[/tex]为 [tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex]阶矩阵，且满足[tex=7.0x1.429]JCI3XqeswtPsEQa0s5EZ64eYUyqk1pqfUL6OTIMe1ZM=[/tex] 及[tex=7.571x1.5]Dx2iaE/u5YIv8AXr5zgnpt/VUHNDJ2UQvyBhqzS2QOE=[/tex], 证明 [tex=7.071x1.0]227z0yrIQDQo21wqgYTp/s5H7bObJU+z792/EHE0gHQ=[/tex]