利用初等变换求下列方阵的逆矩阵
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利用初等变换求下列方阵的逆矩阵
{ 3,-2,0,-1
0,2,2,1,
1,-2,-3,-2
0 1 2 1}
{ 3,-2,0,-1
0,2,2,1,
1,-2,-3,-2
0 1 2 1}
![利用初等变换求下列方阵的逆矩阵](/uploads/image/z/12067106-50-6.jpg?t=%E5%88%A9%E7%94%A8%E5%88%9D%E7%AD%89%E5%8F%98%E6%8D%A2%E6%B1%82%E4%B8%8B%E5%88%97%E6%96%B9%E9%98%B5%E7%9A%84%E9%80%86%E7%9F%A9%E9%98%B5)
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
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