求解矩阵方程AX=B

Question

A={123/221/343} B={1 -1/0 3/1 0}

Answer 1

AX=B即
1 2 3 1 -1
2 2 1 0 3
3 4 3 1 0 r2-2r1,r3-3r1
～
1 2 3 1 -1
0 -2 -5 -2 5
0 -2 -6 -2 3 r1+r2,r3-r2,r2*(-1),r3*(-1)
~
1 0 -2 -1 4
0 2 5 2 -5
0 0 1 0 2 r1+2r3,r2-5r3,r2/2
~
1 0 0 -1 8
0 1 0 1 -15/2
0 0 1 0 2
于是解得X=
-1 8
1 -15/2
0 2