求矩阵的逆(0 0 1 -1 ,0 3 1 4 ,2 7 6 -1,1 2 2 -1)

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求矩阵的逆(0 0 1 -1 ,0 3 1 4 ,2 7 6 -1,1 2 2 -1)
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求矩阵的逆(0 0 1 -1 ,0 3 1 4 ,2 7 6 -1,1 2 2 -1)
求矩阵的逆(0 0 1 -1 ,0 3 1 4 ,2 7 6 -1,1 2 2 -1)

求矩阵的逆(0 0 1 -1 ,0 3 1 4 ,2 7 6 -1,1 2 2 -1)
(A,E)=
0 0 1 -1 1 0 0 0
0 3 1 4 0 1 0 0
2 7 6 -1 0 0 1 0
1 2 2 -1 0 0 0 1
r2-r1,r3-6r1,r4-2r1
0 0 1 -1 1 0 0 0
0 3 0 5 -1 1 0 0
2 7 0 5 -6 0 1 0
1 2 0 1 -2 0 0 1
r3-2r4
0 0 1 -1 1 0 0 0
0 3 0 5 -1 1 0 0
0 3 0 3 -2 0 1 -2
1 2 0 1 -2 0 0 1
r2-r3,r3*(1/3),r2*(1/2)
0 0 1 -1 1 0 0 0
0 0 0 1 1/2 1/2 -1/2 1
0 1 0 1 -2/3 0 1/3 -2/3
1 2 0 1 -2 0 0 1
r4-2r3
0 0 1 -1 1 0 0 0
0 0 0 1 1/2 1/2 -1/2 1
0 1 0 1 -2/3 0 1/3 -2/3
1 0 0 -1 -2/3 0 -2/3 7/3
r1+r2,r3-r3,r4+r2
0 0 1 0 3/2 1/2 -1/2 1
0 0 0 1 1/2 1/2 -1/2 1
0 1 0 0 -7/6 -1/2 5/6 -5/3
1 0 0 0 -1/6 1/2 -7/6 10/3
交换行
1 0 0 0 -1/6 1/2 -7/6 10/3
0 1 0 0 -7/6 -1/2 5/6 -5/3
0 0 1 0 3/2 1/2 -1/2 1
0 0 0 1 1/2 1/2 -1/2 1
A^-1 =
-1/6 1/2 -7/6 10/3
-7/6 -1/2 5/6 -5/3
3/2 1/2 -1/2 1
1/2 1/2 -1/2 1

A^-1 =
-1/6 1/2 -7/6 10/3
-7/6 -1/2 5/6 -5/3
3/2 1/2 -1/2 1
1/2 1/2 -1/2 1