举一反三
- 设 [tex=4.714x1.214]tLAE7Fd4TTuXTyOWoS2OkQ==[/tex] 均为 [tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex] 阶可逆矩阵, 则 [tex=6.071x1.714]MJLEKlCFr3lYK0YSOij+o+qR+f6vv4cFFZ6RlwejfwVsyew60zvd7VOhYD7vpPSZ[/tex] 为 未知类型:{'options': ['[tex=2.786x1.143]Px4s+PosevWooBpZPidJvg==[/tex]', '[tex=2.143x1.143]uxuj4JKb9VGsHYosFYrLAg==[/tex]', '[tex=4.0x1.5]iQ6f5dOu+a42wua+EIUoCQ==[/tex]', '[tex=5.571x1.5]BFEs/LMX6Pti1w68uS/QVZ7Lrbge3U27Pfj3kBdcayA=[/tex]'], 'type': 102}
- 已知3阶矩阵A与3维列向量 x 满足[tex=6.857x1.357]zd0nq0IiNsY0hFTyLJHQy4eC+A8zUY14VqChcVve0aM=[/tex],且向量组[tex=0.714x0.786]Qp78QkdFrqytlOsANWrP9w==[/tex],[tex=3.5x1.429]c2YtesCJSYo0KOSy0rMECg==[/tex] (1)记[tex=10.643x1.357]3tyZrBE07WCx0ZFK2Y3aVjbjYUrJ/5Q0lIjkUE1dgc8=[/tex],求三阶矩阵B,使AP= PB;(2)求[tex=1.357x1.357]0awZUhfhOcjHk6LSkdT6Gw==[/tex]
- 已知 [tex=0.714x0.786]6aVdGcNDEBq8XNsxxe6TUKJi2/iXUJ0aYNv4lG2aSNE=[/tex] 阶矩阵 [tex=1.214x1.214]YsxUk3RpCEL54ROD5kt0RPPW2XVtvzeiNWo/2wW/eZ8=[/tex] 满足 [tex=6.786x1.429]vmxpVoBdkeQ0aONeiDqG8dQ+OFyX3OQLHx1tTsiFx8U=[/tex] 求证: [tex=1.214x1.214]YsxUk3RpCEL54ROD5kt0RPPW2XVtvzeiNWo/2wW/eZ8=[/tex] 可逆,并求 [tex=1.714x1.214]iQ/iEbsDm/5Je+BSznZxUQ==[/tex].
- 设n阶矩阵A 与s阶矩阵B都可逆,求[tex=5.929x2.929]075gCzZzsMRb6HYXYk9X95BT8z7z4e+4OInb7Y8WX7mlX1JqGvQbOIoyVZF9LvTxogPvhwFUoE0aUeAMjFCx5w==[/tex]
- 设n阶矩阵A 与s阶矩阵B都可逆,求[tex=5.929x2.929]075gCzZzsMRb6HYXYk9X9wnlXBOdM81Ai4VHwyypbkMOsILM5b5DtPOUEDyBPeKjBLxoeS2aWJk35clIXAe1sw==[/tex],
内容
- 0
设 [tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex] 是可逆矩阵,且 [tex=4.0x1.5]BEd7xU869/Q07FEvsCiQzQ==[/tex] ,证明 [tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex] 的伴随矩阵 [tex=2.714x1.071]McimwScaoPKtg/1CIv4Smg==[/tex] .
- 1
设矩阵[tex=8.929x4.214]4HdNp+8uldlFnb2+0zUGRZpWMiC6LJlrizg2rAM2YkYeL7ogK2QK4sjDe9gS98VOvP0zOalQPslR14HhEa+/wCJvJrsYvxxBIaf4oVQzhUwj+lLKSmsUDnNu5vdSmC04sTaend2emWdJlaoJ+ODvG4iRP9CkFcLslZQUGhRrHWaVvWHGOpwBteeDF3a5d6jENL8Z+htESrRmja1+B3DSzQ==[/tex]相似与矩阵[tex=7.714x4.214]wK/tDmUX/6mGW6f2tpIfaiHdmphAsRy/CiVjv5pMAT/WYIm1k312z92k806Bl73i9nFMb1LVVj5Xr1v2741Ry9R0wjfRn+2t9SAS5B3cLHAlqEnwVVt+W9SRDtKkcZngQA6paMgN3qTILW2Zj8j/ZHz9zdloBDp2+1wrrrpHkku3GskG7dG7RsYt3aMUpg9wJO7PmvZyUENB9rSC0Y9ALA==[/tex],(I)求[tex=1.429x1.286]+fmtub6g+tF54Tl5ap2zBg==[/tex]的值;(II)求可逆矩阵[tex=0.786x1.286]9wg+6a7IACk0JLAiQsDfSw==[/tex],使[tex=3.5x1.286]S/RTnKAtWmzhhpxNqEOvRLfbrSLY5b9PJVPoUf3hJys=[/tex]为对角矩阵。(本题满分11分)
- 2
已知[tex=1.786x1.214]IENxQEh5u4RdnCaqHm72Xg==[/tex]为3阶矩阵,且[tex=6.5x1.357]Xw38Dcvrbs7IEKOZRvkd5g==[/tex],其中[tex=0.786x1.0]XvHgf70VtK2FH5G93l0k3g==[/tex]是3阶单位矩阵.(1)证明:矩阵[tex=2.786x1.143]RcZ2ZRIlzxNTbD8lUHAX+Q==[/tex]可逆;(2)若[tex=7.786x3.5]DgXZT9CtCPAglTYwc4pEdVwGPrEvfplbNSz07f1CHm3lKZFzRkIi88nqRWCa7cdxtDn1Uq6Au4bDH+3NSK9+pGWuIrunnKgMXUiXxap7tYqS5e4P0ZLrWW76zZyDl/um[/tex],求矩阵[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]
- 3
已知[tex=13.714x1.357]EPxYqhTHgRcZrCT8hpvoe+Su1KT1gXlW8GJHAoFJDpz7VviovI+zTZxRNw5PeSua[/tex]求 [tex=2.786x1.214]iQbgMqjoAzxOFWjVlhQ/IQ==[/tex]
- 4
设 [tex=2.786x1.214]iQbgMqjoAzxOFWjVlhQ/IQ==[/tex] 都是 [tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex] 阶矩阵, [tex=1.786x1.214]s/df2ZE+BhF7kkKI1Rb3ww==[/tex] 各有 [tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex] 个不同的特征值, 又 [tex=1.857x1.357]16KT0+hXCf8wMIstCDilkg==[/tex]是 [tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex] 的特征多项式, 且 [tex=2.071x1.357]20lFRzgrG4cdjOfs4Ad43w==[/tex] 是可逆矩阵. 求证: 矩阵 [tex=6.929x2.786]gnJdtx18Gteda4cw1elCaw1rz7PGYBU/xDTd1JTsuspF7aiAA42OHoV6hWfd0gGeCfm3ufa2hbIwfH2qyHHz+O8XZbDcrmgiTrA5HwaAVIA=[/tex] 相似于对角矩阵.