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

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

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

0 0 5 3 1 -2 -3 0

0 0 -2 -1 0 1 0 -2

1 0 -1 -1 0 1 1 0

0 1 2 1 0 0 0 1

r1+2r2, r4+r2

0 0 1 1 1 0 -3 -4

0 0 -2 -1 0 1 0 -2

1 0 -1 -1 0 1 1 0

0 1 0 0 0 1 0 -1

r2+2r1, r3+r1

0 0 1 1 1 0 -3 -4

0 0 0 1 2 1 -6 -10

1 0 0 0 1 1 -2 -4

0 1 0 0 0 1 0 -1

r1-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

交换行得

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

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