用矩阵的初等变换求逆矩阵:A=0,0,1,2;1, - 知识问答

用矩阵的初等变换求逆矩阵:A=0,0,1,2;1,0,2,0;0,1,0,2;2,1,0,0

1个回答

0 0 1 2 1 0 0 0
1 0 2 0 0 1 0 0
0 0 1 0 0 0 1 0
2 1 0 0 0 0 0 1
r4-2r2
0 0 1 2 1 0 0 0
1 0 2 0 0 1 0 0
0 0 1 0 0 0 1 0
0 1 -4 0 0 -2 0 1
r1-r3,r2-2r3,r4+4r3
0 0 0 2 1 0 -1 0
1 0 0 0 0 1 -2 0
0 0 1 0 0 0 1 0
0 1 0 0 0 -2 4 1
交换行得
1 0 0 0 0 1 -2 0
0 1 0 0 0 -2 4 1
0 0 1 0 0 0 1 0
0 0 0 2 1 0 -1 0
r4*1/2
1 0 0 0 0 1 -2 0
0 1 0 0 0 -2 4 1
0 0 1 0 0 0 1 0
0 0 0 1 1/2 0 -1/2 0
右边就是A的逆了
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