Question

设矩阵A为3阶方阵,|A|=-2,把A按列分块A=(A1,A2,A3),其中Aj(j=1,2,3)为A的第j列

Answer 1

（1）|A1,-3A3,A2|

=3*|A1,-A3,A2|

=3*(-1)*|A1,A2,-A3|

=3*(-1)*(-1)*|A1,A2,A3|

=3*(-1)*(-1)*(-2)

=-6

(2)|A3-3A1,2A2,A1|

=|A3,2A2,A1|

=(-1)|A1,2A2,A3|

=(-1)*2*|A1,A2,A3|

=(-1)*2*(-2)

=4