用初等变换求下列矩阵的逆矩阵(3 -1 0 5 ⼀2 0 5 0⼀3 1 5 4⼀3 0 5 2)

(A,E)=
3 -1 0 5 1 0 0 0
2 0 5 0 0 1 0 0
3 1 5 4 0 0 1 0
3 0 5 2 0 0 0 1

r4-r2
3 -1 0 5 1 0 0 0
2 0 5 0 0 1 0 0
3 1 5 4 0 0 1 0
1 0 0 2 0 -1 0 1

r1-3r4,r2-2r4,r3-3r4
0 -1 0 -1 1 3 0 -3
0 0 5 -4 0 3 0 -2
0 1 5 -2 0 3 1 -3
1 0 0 2 0 -1 0 1

r3+r1, r1*(-1)
0 1 0 1 -1 -3 0 3
0 0 5 -4 0 3 0 -2
0 0 5 -3 1 6 1 -6
1 0 0 2 0 -1 0 1

r3-r2
0 1 0 1 -1 -3 0 3
0 0 5 -4 0 3 0 -2
0 0 0 1 1 3 1 -4
1 0 0 2 0 -1 0 1

r1-r3,r2+4r3,r4-2r3
0 1 0 0 -2 -6 -1 7
0 0 5 0 4 15 4 -18
0 0 0 1 1 3 1 -4
1 0 0 0 -2 -7 -2 9

r2*(1/5), 交换行
1 0 0 0 -2 -7 -2 9
0 1 0 0 -2 -6 -1 7
0 0 1 0 4/5 3 4/5 -18/5
0 0 0 1 1 3 1 -4

所以A^-1=
-2 -7 -2 9
-2 -6 -1 7
4/5 3 4/5 -18/5
1 3 1 -4

自己动点脑子吧