• 2022-05-29
    设A,B,C均为n阶矩阵,若由AB=AC能推出B=C,则A应满足()[tex=17.071x1.357]KFLjEEKUndELza/jfsvedZlhVwZhgfSd+4p6fCo9bUsfYZUunUKD3Hyi08hbCxYaoWTI7Mbt3N2MnYPHFV/mng==[/tex]
  • (A)反例:[tex=47.857x2.786]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[/tex],但B≠C.(B)反例:设[tex=29.5x2.786]tAg4kjefm91yBdigy4ffjFiindG/3VafAJ4ywv+nNHBUKbsghd8Oixp2wA8XHBZcQ7yTPq3bP4v6uKbVVJEa0s8j/gGaCscdc5Z7oZSt4GAEEuyg1O6+fHf6Y5u6idGHJjS6wnc5pcYJgAm0+pC+6EnBJ4xaKEVqmbpKEKTG9QjhsfdLGsOowycK2Itoc5jQrJDc4mR4QCA45CMBFFXuX1rD/2ZZ88JQqjFsCQ/NX8Fgf6Ua0gANTYbqWxsgfCBodNYwsTvfa/d0ZYyWsc+Eks+KuGRk2wBQPXLxSnzgloyNsmWh0YCcOWcpf6pgrpydzawLczokNbojZKzE6kyzSg==[/tex],但B≠C.(C)|A|≠0,则A可逆,那么有[tex=7.143x1.214]QJyKYdgABfIx1A3BxCDrEFUY91yhjGI93AWJ3Dg1y5U=[/tex],即B=C.(D)反例:设[tex=27.143x2.786]sSXBpxJWudVpH1R35o4LnDeQa+3qdZGSRmB/hnqytd2haxLlFK0IrkN5EF3+5eil/D1Jqwx5rrWGZmAN3smCVxK5Lpm4W9pB5tXknJbEKDdb4X1XXL8v+achbJsiTwMkWEzS9mG6UDh6U7uYNt+M7vhxcOXMPleTQoCh42t5J1f4UwR2fCnra32jZRAv/5F7ZEgYO6dpsNOjvSHxDthKNwrChogARZGX9fD7j4rVv/8ckqkB+RLTLkMayEZi7hp93/MZ2+qv+lrUfZ5HUOXy9g==[/tex]但B≠C.故本题应选(C).

    内容

    • 0

      设A,B均为n阶矩阵,|A|=2,|B|=-3,则|2A*B-1|_______。

    • 1

      设A,B均为n阶矩阵,|A|=2,|B|=-3,则|2A*B^T|=?

    • 2

      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

    • 3

      设A为n阶方阵,若对任意n×m(m≥n)矩阵B都有AB=0,则A=()。 A: 0 B: 1 C: 2 D: 3

    • 4

      设A,B,C均为n阶方阵,且AB=AC,则()