Question

已知A=（1 3 -4 ,1 3 -5,-1 -4 6 ）,求A的逆矩阵

Answer 1

(A,E)=

1 3 -4 1 0 0

1 3 -5 0 1 0

-1 -4 6 0 0 1

r2-r1,r3+r1

1 3 -4 1 0 0

0 0 -1 -1 1 0

0 -1 2 1 0 1

r1-4r2,r3+2r2,r2*(-1)

1 3 0 5 -4 0

0 0 1 1 -1 0

0 -1 0 -1 2 1

r1+3r3,r3*(-1)

1 0 0 2 2 3

0 0 1 1 -1 0

0 1 0 1 -2 -1

r2r3

1 0 0 2 2 3

0 1 0 1 -2 -1

0 0 1 1 -1 0

所以A^-1=

2 2 3

1 -2 -1

1 -1 0