Question

已知矩阵AB=A+2B,求B

矩阵A=
0,3,3
1,1,0
-1,2,3

Answer 1

解: 由 AB=2B+A 得 (A-2E)B = A
(A-2E, A) =
-2 3 3 0 3 3
1 -1 0 1 1 0
-1 2 1 -1 2 3

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

r2+r1,r3-r1
0 1 3 2 5 3
1 0 3 3 6 3
0 0 -2 -2 -2 0

r3*(-1/2), r1-3r3,r2-3r3
0 1 0 -1 2 3
1 0 0 0 3 3
0 0 1 1 1 0

交换行
1 0 0 0 3 3
0 1 0 -1 2 3
0 0 1 1 1 0

B =
0 3 3
-1 2 3
1 1 0

追问

(A-2E,A)是什么意思呀