Question

矩阵A=(-2 3 3,1 1 0, -1 2 1)的逆矩阵怎么求的? 谢谢了.

Answer 1

解: (A,E) =
-2 3 3 1 0 0
1 1 0 0 1 0
-1 2 1 0 0 1

r1-2r3,r3+r2
0 -1 1 1 0 -2
1 1 0 0 1 0
0 3 1 0 1 1

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

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

r1+r3,r2-r3
0 1 0 -1/4 1/4 3/4
1 0 0 1/4 3/4 -3/4
0 0 1 3/4 1/4 -5/4

r1<->r3
1 0 0 1/4 3/4 -3/4
0 1 0 -1/4 1/4 3/4
0 0 1 3/4 1/4 -5/4

所以 A^-1 =
1/4 3/4 -3/4
-1/4 1/4 3/4
3/4 1/4 -5/4

Answer 2

inv(A)