设A、B为三阶矩阵,且|A|=2,|B|=3,求|-2(A^T B^-1)^-1|

括号里是:A的T次方再乘以B的负一次方
2025-06-27 15:18:05
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回答1:

|-2(A^T B^-1)^-1|
=(-2)^3 |(A^T B^-1)^-1|
= -8 |(A^T B^-1)|^-1
= -8 |A^T|^-1 |B^-1|^-1
= -8 |A|^-1 |B|
= -8 x (1/2) x 3
= -12.