Question

若三阶矩阵A的伴随矩阵A*,已知|A|=1/2,求|（3A）^-1-2A*|的值

Answer 1

|（3A）^-1-2A*|=|1/3(A^-1)-2A*|

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

=|2/3(A*)-2(A*)|

=|-4/3(A*)|

=(-4/3)^3|A*|

=(-64/27)|A|^2

=(-64/27)(1/4)

=-16/27 答案补充 AA*=|A|E

|A*|=|A|^n-1