设A=|4 2 3 ,1 1 0,-1 2 3 |,且矩阵X满足AX=A+2X,求X
问题描述：
设A=|4 2 3 ,1 1 0,-1 2 3 |,且矩阵X满足AX=A+2X,求X
答
由 AX=A+2X 得 (A-2E)X = A.(A-2E,A) =2 2 3 4 2 31 -1 0 1 1 0-1 2 1 -1 2 3r1-2r2,r3+r20 4 3 2 0 31 -1 0 1 1 00 1 1 0 3 3r1-4r3,r2+r30 0 -1 2 -12 -91 0 1 1 4 30 1 1 0 3 3r2+r1,r3+r1,r1*(-1)0 0 1 -2 12 91...