设n阶矩阵A 与s阶矩阵B都可逆,求[tex=5.929x2.929]075gCzZzsMRb6HYXYk9X9wnlXBOdM81Ai4VHwyypbkMOsILM5b5DtPOUEDyBPeKjBLxoeS2aWJk35clIXAe1sw==[/tex]，
求[tex=5.0x2.786]075gCzZzsMRb6HYXYk9X92zk8W4u1qJBIO8aFf+ZsZwaC6mXHyaO42ZZFn3Y5ty/bl398sgfwaZ/eyLMCQdRdA==[/tex]的逆阵，就是求[tex=1.857x1.071]59Lf0ZARIvhNwNVgce8j1g==[/tex]阶方阵X，使[tex=9.214x2.786]075gCzZzsMRb6HYXYk9X96c14hJEyYCrY/NHnamm9Axv3wj6cDXa/m0w59qdSbnGORVnLZw0ipt9bsnZC/QIfTqebN5qQ5h5IoHPHJmWEsDrKwrM6Rsd08W6HukTXbTVn87UOkTMiu6NSEQr400gYIcT0ckVdnbCBRf4RUeyxuObAIiPa+s/6EIGENqilLDjrOmXX48D25cJCyngx1mh1A==[/tex]（2.6）为此，根据原矩阵的分块情况，对X作一样的分块，[tex=8.357x2.786]WJjqTt+wsb5RrYXOGySYfzj6I8kiWIUfzTYtvJSg6gpVziyJtX+BeQj/QE3W1XPUdPk4uNiS1Re391W6SYR86yuNCfTMka72++yoNgseIKA=[/tex]，其中[tex=7.929x1.214]ZL4OSwbgka8hhT6CpJpo0U13NwBFNaBb8Dv5s5UsR/4NcDMQP10vqRl31QIHvJWk7eUXdBZWBltF7ch3nf+C9VN798I6VAOBjUOL6fcAjviscL0wX5ZB5WDoVwvqKRDQ[/tex]是未知矩阵（为明确起见，它们依次是[tex=7.929x1.143]IlEBKyNO6l8NXxXMF4uLOuy1OQvuT0jvhsXWDX7Gi5UW5zBcA32QNAqq2+SRw6OJ[/tex]，[tex=2.214x1.071]G07CJOBPHYLv5EmeZPLTIQ==[/tex]矩阵），把上式代入（2.6）式得到[tex=35.214x2.929]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[/tex]比较上式两端两个矩阵，有[tex=10.071x1.429]XBVVFc8VWJdGLhoNySHwLIcacSIBY2LtdOUPpPnv+N01Gm/a6XK1we5b8TEO5Y4G[/tex][tex=8.5x1.214]lnIAvR2oO5RJxBdbKJblFQwMPwwrq1Wj/7P+8ufj7Xo=[/tex][tex=18.5x1.429]APjDUlJa9hGmRkyRN7eSncHs/SqkXxEoTcXnKMmZxKgmqj9ATp6EBvJMEvLU+pi9IDyYbtiaFSEfxJRfulQkD5RbEVkIWq7CJIOoG/6qBqs=[/tex][tex=28.857x1.429]XLdlUhm36audm8RUpqgFPHTVPR5Lvui8xrVjTbNQIKCbH/DaTl/RguVv8MuNGq6T6/uRgzaGcvYXDDjh9EtqSbLP2yfGLLmj7H9EI9Joqk8DJyLOyKC6GADjZPBTskH6EYsdEDONOV3O8J4oTx5xSo+/Rxfpbh26zWr2n+uDrdtGR261Y88KPinH+p4OMJePrQWQTve9Ikflr0bpLqloxJ+5ONofsXP8O1umdxUQalJ+i7hkqF6S5+5SSycKJ0PfSOTFEGA6+fd4W5He5qAtRz7vcjzLGbTzukaDbNvw+mo=[/tex]于是得[tex=19.5x3.0]075gCzZzsMRb6HYXYk9X96c14hJEyYCrY/NHnamm9Axv3wj6cDXa/m0w59qdSbnGORVnLZw0ipt9bsnZC/QIfTqebN5qQ5h5IoHPHJmWEsDrKwrM6Rsd08W6HukTXbTVncEmYPN+kyS2CJL6gsQ185RTKHH7hD2W6qCD+NY0wvKY1Fy+6WN3l9bos6VEH7yZgUEtVTIJUSitHlknlvjuyNJ55tIGAMAlZ3M1QjKmkguOvOU0FxM15tJikUCIU6AWdIEnrxdTpzmxlSSKWi05NTFQ4ehJO9vxXxt7FK5A1vkjCU/Dm4z0Vn2U/c1NIAqYmZgV9qQ/fYpeqOB6J7VjT4/AYavXC/LEDI9qGaD4fKgiiPGB3liffyyTe8mi/d+q[/tex]
举一反三
- 设n阶矩阵A 与s阶矩阵B都可逆,求[tex=5.929x2.929]075gCzZzsMRb6HYXYk9X95BT8z7z4e+4OInb7Y8WX7mlX1JqGvQbOIoyVZF9LvTxogPvhwFUoE0aUeAMjFCx5w==[/tex]
- 设[tex=0.643x1.286]Nud/2eskX2OmQOds9nx+Fw==[/tex]阶矩阵[tex=0.786x1.286]pi/GsQ3apuRt43V3XQq/tA==[/tex]及[tex=0.5x1.286]r65Ank8E1dV+BtDCLn5S+w==[/tex]阶矩阵[tex=0.786x1.286]q1djlrfSWHAqH21hBgtrSw==[/tex] 都可逆, 求(1)[tex=5.929x2.929]rwMhqGKFQ+j3l2qMx/grPmtqXebwM7lRAV7uUT8ea0FCL1MAiTkcIUmbpKZBtEflME05K6QZLyCpaaEi/cmy2NOaEElFekXmtlEtJzfu/3o=[/tex]; (2)[tex=5.929x2.929]rwMhqGKFQ+j3l2qMx/grPqH4onJbyJSuN9BDoj1IoCp3XXc+tuCZRRR1rFYfdwjr+mbUYeI53nhkQMNOXv1vJDNsBVTUq4z8ki3uzTpao7M=[/tex].
- 设[tex=7.071x2.929]r+tiAx6ClSaeP7cZbqpjmXACNCkTkLbXSmdm65cOw+XEpcgk96uDO4lIHcqlGaczSOLNcuYH7zqrd49WI1GD1U4kYe0GU4X7fhxjEj8PY0o=[/tex]，其中B是n阶可逆矩阵，C是m阶可逆矩阵，证明A可逆，并求[tex=1.714x1.286]TO1yVSeu6VTkH5eqe0g3AQ==[/tex]。
- 设[tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex]阶矩阵[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]及[tex=0.929x0.786]VF0GLe2VBE/4VKNzpyOfFg==[/tex]阶矩阵[tex=0.786x1.0]sHo1pKm+gjxjcUAJjHrarQ==[/tex]都可逆，求:[br][/br][tex=5.929x2.929]jcCMHflCR8OS9TosV6N5vF5TBJ+hnWfKaPJMOj8+lW0ygKrP6wzvVGy4qDOEHs7MmQbphQ3QGPzl+GgH9R2nuUXdv9OFV78Y/zQ8LkM9gwU=[/tex]
- 设[tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex]阶矩阵[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]及[tex=0.929x0.786]VF0GLe2VBE/4VKNzpyOfFg==[/tex]阶矩阵[tex=0.786x1.0]sHo1pKm+gjxjcUAJjHrarQ==[/tex]都可逆，求:[br][/br] [tex=5.929x2.929]jcCMHflCR8OS9TosV6N5vBtqjFrNFsn83APbaxuqgln63xB3nfahLwrMM85/LxtPiUi2rhRjG7dK5tvmUaNfzVRWRWHvWd+Bwo8bb86k1ZY=[/tex]
内容
- 0
设A，B均为4阶矩阵，且|A|=3，|B|=-2，则|-(A′B-1)2|的值为()。 A: 9/5 B: 9/4 C: 7/5 D: 9/2
- 1
设AB都是n阶矩阵,|A|=4,|B|=5,求|AB|
- 2
设λ是n阶矩阵A的一个特征值（1）求矩阵[tex=6.786x1.429]tlgj5USZTf2WNtmUi8mi5sa/mE7EdNSlMCrYvVYZoHM=[/tex]的一个特征根；（2）若A可逆，求[tex=8.643x1.571]/zeZGLwofF7n+e9PBZc4i2L0OfKt89EacJI1MGhwA/t9T00iSnnaoID99f0962bxwHWzOdN8CAj7JuM9T+4Jes1XCwP6R0NSA4bAgR7qzWWwdDPn6Nn677hxeosgYHNY[/tex]的一个特征根.
- 3
设A为3阶矩阵，|A|=-3,则|3A|=（ ） A: 9 B: -9 C: 81 D: -81
- 4
设n阶矩阵及s阶矩阵都可逆,则为( )5592a37ae4b0ec35e2d3a91e.gif5592a06ae4b0ec35e2d3a6af.gifabc3a7beb591cf49723360f235001a71.gif