3×3矩阵A=｛4,2,3,1,1,0,-1,2,3｝,AB=A+2B,求B如题,A=｛4 2 3 1 1 0 -1 2 3｝AB=A+2B,求B
问题描述：
3×3矩阵A=｛4,2,3,1,1,0,-1,2,3｝,AB=A+2B,求B
如题,A=｛4 2 3
1 1 0
-1 2 3｝
AB=A+2B,求B
答
(3,-8,-6;2,-9,-6;-2,12,9)
答
解:AB=A+2B,(A-2E)B=A,B=(A-2E)^(-1)A,
(A-2E)^(-1)={1,-4,-3;1,-5,-3;-1,6,4},
B=(A-2E)^(-1)A={3,-8,-6;2,-9,-6;-2,12,9}.
答
AB=A+2B
AB-2B=A
AB-2EB=A
(A-2E)B=A
[(A-2E)^(-1)](A-2E)B=[(A-2E)^(-1)]A
EB=[(A-2E)^(-1)]A
B=[(A-2E)^(-1)]A
B=[(A-2E)*]A/│A-2E│
B=(3,-8,-6;2,-9,-6;-2,12,9)