Question

已知a为三阶方阵,且|a|=-2,求1.|(2a)^(-1)| 2.|a*-0.5a^-1)|

Answer 1

1.|(2A)^-1|

= |(1/2)A^-1|

= (1/2)^3 |A|^-1

= (1/8)*(-1/2)

= -1/16.

2.|A*-0.5A^-1|

= ||A|A^-1-0.5A^-1|

= |-2.5A^-1|

= (-2.5)^3 |A|^-1

= (-2.5)^3 * (-1/2)

= 125/16.