Question

高数 求解过程

Answer 1

首先得到A-2E=
-1 1 -1
-1 -1 1
1 -1 -1
那么再使用初等行变换的方法，求逆矩阵
A-2E,E=
-1 1 -1 1 0 0
-1 -1 1 0 1 0
1 -1 -1 0 0 1 r1+r2,r2+r3
~
-2 0 0 1 1 0
0 -2 0 0 1 1
1 -1 -1 0 0 1 r1/-2，r2/-2
～
1 0 0 -1/2 -1/2 0
0 1 0 0 -1/2 -1/2
1 -1 -1 0 0 1 r3-r1,r3+r2,r3*-1
~
1 0 0 -1/2 -1/2 0
0 1 0 0 -1/2 -1/2
0 0 1 -1/2 0 -1/2
所以得到A-2E的逆矩阵为
-1/2 -1/2 0
0 -1/2 -1/2
1/2 0 -1/2