Question

求矩阵3 -1 2 ,1 4 -3,2 2 1的逆矩阵 急

Answer 1

(A,E)=
3 -1 2 1 0 0
1 4 -3 0 1 0
2 2 1 0 0 1
r1-3r2,r3-2r2
0 -13 11 1 -3 0
1 4 -3 0 1 0
0 -6 7 0 -2 1
r1-2r3
0 -1 -3 1 1 -2
1 4 -3 0 1 0
0 -6 7 0 -2 1
r2+4r1,r3-6r1
0 -1 -3 1 -3 -2
1 0 -15 -4 13 8
0 0 25 -6 -8 13
r1*(-1),r3*(1/25),r1-3r3,r2+15r3
1 0 0 2/5 -7/5 -1/5
0 1 0 -7/25 27/25 11/25
0 0 1 -6/25 16/25 13/25
所以 A^-1=
2/5 -7/5 -1/5
-7/25 27/25 11/25
-6/25 16/25 13/25