3 0 -1 设A= 1 4 1 ,求矩阵B,使得AB-2A=2B.1 0 3
人气：220 ℃ 时间：2020-10-01 08:41:57
解答
由AB-2A=2B
得 (A-2E)B=2A
(A-2E,A) =
1 0 -1 3 0 -1
1 2 1 1 4 1
1 0 1 1 0 3
r2-r1,r3-r1
1 0 -1 3 0 -1
0 2 2 -2 4 2
0 0 2 -2 0 4
r2*(1/2),r3*(1/2),
1 0 -1 3 0 -1
0 1 1 -1 2 1
0 0 1 -1 0 2
r1+r3,r2-r3
1 0 0 2 0 1
0 1 0 0 2 -1
0 0 1 -1 0 2
2 0 1 4 0 2
所以有 B = 2(A-2E)^-1A= 2* 0 2 -1 = 0 4 -2
-1 0 2 -2 0 4
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