Question

用初等矩阵求逆矩阵

Answer 1

(A,E)=

1 2 2 1 0 0

2 1 -2 0 1 0

2 -2 1 0 0 1

r2-2r1,r3-2r1

1 2 2 1 0 0

0 -3 -6 -2 1 0

0 -6 -3 -2 0 1

r3-r2

1 2 2 1 0 0

0 -3 -6 -2 1 0

0 0 9 2 -2 1

r2*(-1/3), r3*(1/9)

1 2 2 1 0 0

0 1 2 2/3 -1/3 0

0 0 1 2/9 -2/9 1/9

r2-2r3

1 2 2 1 0 0

0 1 0 2/9 1/9 -2/9

0 0 1 2/9 -2/9 1/9

r1-2r2-2r3

1 0 0 1/9 2/9 2/9

0 1 0 2/9 1/9 -2/9

0 0 1 2/9 -2/9 1/9

所以 A^-1 =

1/9 2/9 2/9

2/9 1/9 -2/9

2/9 -2/9 1/9

= (1/9)A