Question

用初等变换法求逆矩阵2 2 31 -1 0-1 2 1

Answer 1

(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

r1r3

-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