Question

设矩阵A=(1,1,-1;2,1,0;1,1,1），求A-1 （-1是弱小在右上角的）

Answer 1

解: (A,E) =
1 1 -1 1 0 0
2 1 0 0 1 0
1 1 1 0 0 1

r2-r1-r3, r3-r1
1 1 -1 1 0 0
0 -1 0 -1 1 -1
0 0 2 -1 0 1

r2*(-1),r3*(1/2)
1 1 -1 1 0 0
0 1 0 1 -1 1
0 0 1 -1/2 0 1/2

r1-r2+r3
1 0 0 -1/2 1 -1/2
0 1 0 1 -1 1
0 0 1 -1/2 0 1/2

所以 A^-1 =
-1/2 1 -1/2
1 -1 1
-1/2 0 1/2

Answer 2

……是求逆吧
用初等变换就行
A^(-1)={(-1/2,1,-1/2),(1,-1,1),(-1/2,0,1/2)}