Question

已知矩阵A和B满足关系式AB=A+2B,其中A=4 2 3,求B 1 1 0 -1 2 3

Answer 1

因为 AB=A+2B
所以 (A-2E)B = A
(A-2E,A) =
4 2 3 1 0 0
1 1 0 0 1 0
-1 2 3 0 0 1
r1-4r2,r3+r2
0 -2 3 1 -4 0
1 1 0 0 1 0
0 3 3 0 1 1
r3*(1/3),r1+2r3,r2-r3
0 0 5 1 -10/3 2/3
1 0 -1 0 2/3 -1/3
0 1 1 0 1/3 1/3
r1*(1/5),r2+r1,r3-r1
0 0 1 1/5 -2/3 2/15
1 0 0 1/5 0 -1/5
0 1 0 -1/5 1 1/5
交换行
1 0 0 1/5 0 -1/5
0 1 0 -1/5 1 1/5
0 0 1 1/5 -2/3 2/15
X =
1/5 0 -1/5
-1/5 1 1/5
1/5 -2/3 2/15