Question

求行列式的值（1 2 3 2 2 1 3 4 3）的逆矩阵

Answer 1

(A,E)=

1 2 3 1 0 0

2 2 1 0 1 0

3 4 3 0 0 1

r3-r1-r2,r2-2r1

1 2 3 1 0 0

0 -2 -5 -2 1 0

0 0 -1 -1 -1 1

( 由此可得 |A| = 2 )

r1+r2

1 0 -2 -1 1 0

0 -2 -5 -2 1 0

0 0 -1 -1 -1 1

r3*(-1),r1+2r3,r2+5r3

1 0 0 1 3 -2

0 -2 0 3 6 -5

0 0 1 1 1 -1

r2*(-1/2)

1 0 0 1 3 -2

0 1 0 -3/2 3 -5/2

0 0 1 1 1 -1

A的逆 =

1 3 -2

-3/2 3 -5/2

1 1 -1