设矩阵A={1 3 2,1 2 1 ,0 1 0},求A的-1次方是多少?
问题描述:
设矩阵A={1 3 2,1 2 1 ,0 1 0},求A的-1次方是多少?
答
(A,E)=
1 3 2 1 0 0
1 2 1 0 1 0
0 1 0 0 0 1
r1-3r3,r2-2r3
1 0 2 1 0 -3
1 0 1 0 1 -2
0 1 0 0 0 1
r1-r2
0 0 1 1 -1 -1
1 0 1 0 1 -2
0 1 0 0 0 1
r2-r1
0 0 1 1 -1 -1
1 0 0 -1 2 -1
0 1 0 0 0 1
交换行
1 0 0 -1 2 -1
0 1 0 0 0 1
0 0 1 1 -1 -1
A^-1 =
-1 2 -1
0 0 1
1 -1 -1