Question

用初等行变换求矩阵A=2 1 11 1 2 0 1 1求A的-1次方?

Answer 1

(A,E)=

2 1 1 1 0 0

1 1 2 0 1 0

0 1 1 0 0 1

r1-2r2

0 -1 -3 1 -2 0

1 1 2 0 1 0

0 1 1 0 0 1

r1+r3,r2-r3

0 0 -2 1 -2 1

1 0 1 0 1 -1

0 1 1 0 0 1

r1*(-1/2),r2-r1,r3-r1

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

1 0 0 1/2 0 -1/2

0 1 0 1/2 -1 3/2

交换行

1 0 0 1/2 0 -1/2

0 1 0 1/2 -1 3/2

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

A^-1 =

1/2 0 -1/2

1/2 -1 3/2

-1/2 1 -1/2