|112||100|设A=|223|,B=|211|,矩阵X满足AX=B^T.求X|433||-122|1.除了用初等变换来求解,还有什么方法?2.

Question

| 1 1 2 | | 1 0 0 | 设A=| 2 2 3 |,B=| 2 1 1 |,矩阵X满足AX=B^T.求X |4 3 3 | | -1 2 2 |
1.除了用初等变换来求解,还有什么方法?
2.

Answer 1

(A,B^T) =
1 1 2 1 2 -1
2 2 3 0 1 2
4 3 3 0 1 2
r4-4r1,r2-2r1
1 1 2 1 2 -1
0 0 -1 -2 -3 4
0 -1 -5 -4 -7 6
r1+2r2,r3-5r2,r2*(-1)
1 1 0 -3 -4 7
0 0 1 2 3 -4
0 -1 0 6 8 -14
r1+r3,r3*(-1)
1 0 0 3 4 -7
0 0 1 2 3 -4
0 1 0 -6 -8 14
r2r3
1 0 0 3 4 -7
0 1 0 -6 -8 14
0 0 1 2 3 -4
所以 X =
3 4 -7
-6 -8 14
2 3 -4