Question

用初等变换法求逆矩阵

2 2 3
1 -1 0
-1 2 1

Answer 1

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

r1+2r3,r2+r3得
0 6 5 1 0 2
0 1 1 0 1 1
-1 2 1 0 0 1

r1-6r2，r3-r2得
0 0 -1 1 -6 -4
0 1 1 0 1 1
-1 0 -1 0 -2 -1

r2+r1,r3-r1得
0 0 -1 1 -6 -4
0 1 0 1 -5 -3
-1 0 0 -1 4 3

r1<----->r3
-1 0 0 -1 4 3
0 1 0 1 -5 -3
0 0 -1 1 -6 -4

r1*-1，r3*-1
1 0 0 1 -4 -3
0 1 0 1 -5 -3
0 0 1 -1 6 4

故：A的逆矩阵为：
1 -4 -3
1 -5 -3
-1 6 4

Answer 2