Question

求解矩阵方程AX=B，其中A=2 1 -3 B=1 -1 写出具体求解方法 1 2 2 2 0 -1 3 2 -2 5

Answer 1

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

r1-2r2, r3+r2
0 -3 -7 -3 -1
1 2 2 2 0
0 5 4 0 5

r3+2r1
0 -3 -7 -3 -1
1 2 2 2 0
0 -1 -10 -6 3

r1-3r3, r2+2r3
0 0 23 15 -10
1 0 -18 -10 6
0 -1 -10 -6 3

r1*(1/23), r3*(-1)
0 0 1 15/23 -10/23
1 0 -18 -10 6
0 1 10 6 -3

r2+18r1,r3-10r1
0 0 1 15/23 -10/23
1 0 0 40/23 -42/23
0 1 0 -12/23 31/23

交换行得
1 0 0 40/23 -42/23
0 1 0 -12/23 31/23
0 0 1 15/23 -10/23

所以 B =
40/23 -42/23
-12/23 31/23
15/23 -10/23.

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