设矩阵A=(0 1 2)(1 1 -1)(2 4 1)B=(2 -3)(1 5)(3 6 )解矩阵方程AX=次B 急!

2025-06-28 07:32:29
推荐回答(1个)
回答1:

解:
(A,B)=
0 1 2 2 -3
1 1 -1 1 5
2 4 1 3 6

r3-2r2
0 1 2 2 -3
1 1 -1 1 5
0 2 3 1 -4

r2-r1,r3-2r1
0 1 2 2 -3
1 0 -3 -1 8
0 0 -1 -3 2

r1+2r3,r2-3r3,r3*(-1)
0 1 0 -4 1
1 0 0 8 2
0 0 1 3 -2

r1<->r2
1 0 0 8 2
0 1 0 -4 1
0 0 1 3 -2

所以 X=
8 2
-4 1
3 -2