求三阶矩阵的逆矩阵-2113-9-1-572

Question

求三阶矩阵的逆矩阵 -2 1 1 3 -9 -1 -5 7 2

Answer 1

(A,E)=
-2 1 1 1 0 0
3 -9 -1 0 1 0
-5 7 2 0 0 1
r2+r1,r3-2r1
-2 1 1 1 0 0
1 -8 0 1 1 0
-1 5 0 -2 0 1
r1+2r2,r3+r3
0 -15 1 3 2 0
1 -8 0 1 1 0
0 -3 0 -1 1 1
r3*(-1/3),r1+15r3,r2+8r3
0 0 1 8 -3 -5
1 0 0 11/3 -5/3 -8/3
0 1 0 1/3 -1/3 -1/3
交换行
1 0 0 11/3 -5/3 -8/3
0 1 0 1/3 -1/3 -1/3
0 0 1 8 -3 -5
A^-1=
11/3 -5/3 -8/3
1/3 -1/3 -1/3
8 -3 -5