Question

求:初等变换法求逆矩阵的例题带详解的,

Answer 1

求A的逆矩阵,A=

2 2 3

1 -1 0

-1 2 1

(A,E) =

2 2 3 1 0 0

1 -1 0 0 1 0

-1 2 1 0 0 1

r1-2r2,r3+r2

0 4 3 1 -2 0

1 -1 0 0 1 0

0 1 1 0 1 1

r1-4r3,r2+r3

0 0 -1 1 -6 -4

1 0 1 0 2 1

0 1 1 0 1 1

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

0 0 1 -1 6 4

1 0 0 1 -4 -3

0 1 0 1 -5 -3

交换行得

1 0 0 1 -4 -3

0 1 0 1 -5 -3

0 0 1 -1 6 4

所以 A^-1 =

1 -4 -3

1 -5 -3

-1 6 4