Question

用初等变换求下列矩阵的逆矩阵 2 3 1 1 2 0 -1 2 -2

Answer 1

(A,E)=
2 3 1 1 0 0
1 2 0 0 1 0
-1 2 -2 0 0 1

r1-2r2,r3+r2
0 -1 1 1 -2 0
1 2 0 0 1 0
0 4 -2 0 1 1

r2+2r1,r3+4r1,r1*(-1)
0 1 -1 -1 2 0
1 0 2 2 -3 0
0 0 2 4 -7 1

r2-r3,r3*(1/2),r1+r3
0 1 0 1 -3/2 1/2
1 0 0 -2 4 -1
0 0 1 2 -7/2 1/2

交换行
1 0 0 -2 4 -1
0 1 0 1 -3/2 1/2
0 0 1 2 -7/2 1/2

A^-1 =
-2 4 -1
1 -3/2 1/2
2 -7/2 1/2