设A是3阶方阵,|A|=1/2,求|A-(A^(*))^(*)|
问题描述：
设A是3阶方阵,|A|=1/2,求|A-(A^(*))^(*)|
答
A* = | A|A^(-1),|A*| =| A|^3/|A| = |A|^2 = 1/4,(A*)^(-1) =(1/ | A|)A=2A,
(A* )* = | A*|(A*)^(-1) = (1/4)2A=A/2,
|A-(A*)*| = |(1/2)A| = (1/2)^3*(1/2)=1/16.