Question

利用矩阵的初等变换,求方阵的逆阵（3 -2 0 -1 0 2 2 1 1 -2 -3 -2 0 1 2 1）

Answer 1

(A,E) =

3 -2 0 -1 1 0 0 0

0 2 2 1 0 1 0 0

1 -2 -3 -2 0 0 1 0

0 1 2 1 0 0 0 1

r1-3r3

0 4 9 5 1 0 -3 0

0 2 2 1 0 1 0 0

1 -2 -3 -2 0 0 1 0

0 1 2 1 0 0 0 1

r1-4r4,r2-2r4,r3+2r4

0 0 1 1 1 0 -3 -4

0 0 -2 -1 0 1 0 -2

1 0 1 0 0 0 1 2

0 1 2 1 0 0 0 1

r2+2r1,r3-r1,r4-2r1

0 0 1 1 1 0 -3 -4

0 0 0 1 2 1 -6 -10

1 0 0 -1 -1 0 4 6

0 1 0 -1 -2 0 6 9

r1-r2,r3+r2,r4+r2

0 0 1 0 -1 -1 3 6

0 0 0 1 2 1 -6 -10

1 0 0 0 1 1 -2 -4

0 1 0 0 0 1 0 -1

交换行

1 0 0 0 1 1 -2 -4

0 1 0 0 0 1 0 -1

0 0 1 0 -1 -1 3 6

0 0 0 1 2 1 -6 -10

得 A^-1 =

1 1 -2 -4

0 1 0 -1

-1 -1 3 6 2 1 -6 -10