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

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
有问题请消息我或追问第三排是0,1,0,2啊我重做十分感谢呵呵 粗心要不得00121000102001000102001021000001r4-2r200121000102001000102001001 -400 -201r4-r300121000102001000102001000 -4 -20 -2 -11r2-2r1, r4+4r100121000100 -4 -21000102001000064 -2 -11r4*(1/6)0012 1000100 -4-21000102 001000012/3 -1/3 -1/61/6r1-2r4, r2+4r4, r3-2r40010 -1/32/31/3 -1/310002/3 -1/3 -2/32/30100 -4/32/34/3 -1/300012/3 -1/3 -1/61/6交换行得10002/3 -1/3 -2/32/30100 -4/32/34/3 -1/30010 -1/32/31/3 -1/300012/3 -1/3 -1/61/6