已知矩阵A=[(121),(110),|(232)],用初等变换法求A^-1?

Question

已知矩阵A=[(1 2 1),(1 1 0),|(2 3 2)],用初等变换法求A^-1?

Answer 1

(A,E)=
1 2 1 1 0 0
1 1 0 0 1 0
2 3 2 0 0 1
r2-r1,r3-2r1
1 2 1 1 0 0
0 -1 -1 -1 1 0
0 -1 0 -2 0 1
r1+2r3,r2-r3,r3*(-1)
1 0 1 -3 0 2
0 0 -1 1 1 -1
0 1 0 2 0 -1
r1+r2,r2*(-1)
1 0 0 -2 1 1
0 0 1 -1 -1 1
0 1 0 2 0 -1
r2r3
1 0 0 -2 1 1
0 1 0 2 0 -1
0 0 1 -1 -1 1
所以 A^-1 =
-2 1 1
2 0 -1
-1 -1 1