设矩阵A,B满足A=E(1,3)E(5(-2))BE(3,2(1/2)),则有A.B=E(1,3)E(5(-2))BE(3,2(1/2))B.B=E(1,3)E(5(2))AE(3,2(1/2))C.B=E(5(-1/2))E(1,3)AE(3,2(1/2))D.B=E(1,3)E(5(-1/2))AE(3,2(1/2))谁能告诉我选什么么...过程是什么啊==完全不懂呐

Question

设矩阵A,B满足A=E(1,3)E(5(-2))BE(3,2(1/2)),则有
A.B=E(1,3)E(5(-2))BE(3,2(1/2))
B.B=E(1,3)E(5(2))AE(3,2(1/2))
C.B=E(5(-1/2))E(1,3)AE(3,2(1/2))
D.B=E(1,3)E(5(-1/2))AE(3,2(1/2))
谁能告诉我选什么么...过程是什么啊= =完全不懂呐

Answer 1

BA=B+2E
则 B(A-E) = 2E
B = 2(A-E)^-1
A-E =
1 1
-1 1
(A-E)^-1 =
1/2 -1/2
1/2 1/2
B = 2(A-E)^-1 =
1 -1
1 1