Question

用初等变换求逆矩阵!A=3 2 12 4 01 0 3 求（A-2E）的逆

Answer 1

(A-2E,E)=

1 2 1 1 0 0

2 2 0 0 1 0

1 0 1 0 0 1

r1-r3,r2-2r3

0 2 0 1 0 -1

0 2 -2 0 1 -2

1 0 1 0 0 1

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

0 1 0 1/2 0 -1/2

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

1 0 1 0 0 1

r3-r2

0 1 0 1/2 0 -1/2

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

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

交换行

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

0 1 0 1/2 0 -1/2

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

(A-2E)^-1=

-1/2 1/2 1/2

1/2 0 -1/2

1/2 -1/2 1/2