用初等变换求逆矩阵[1-11/110/211]1-11110211用[A|E]=[E|A∧-1]的方法

Question

用初等变换求逆矩阵[1 -1 1/1 1 0/2 1 1]
1 -1 1
1 1 0
2 1 1用[A|E]=[E|A∧-1]的方法

Answer 1

(A,E)=
1 -1 1 1 0 0
1 1 0 0 1 0
2 1 1 0 0 1
r3-r1
1 -1 1 1 0 0
1 1 0 0 1 0
1 2 0 -1 0 1
r1-r2,r3-r2
0 -2 1 1 -1 0
1 1 0 0 1 0
0 1 0 -1 -1 1
r1+2r3,r2-r3
0 0 1 -1 -3 2
1 0 0 1 2 -1
0 1 0 -1 -1 1
交换行
1 0 0 1 2 -1
0 1 0 -1 -1 1
0 0 1 -1 -3 2
A^-1 =
1 2 -1
-1 -1 1
-1 -3 2