【线性代数】已知矩阵X与A满足关系式,AX=A+X,求X

AX=A+X(A-E)X=A| 0 2 1 || 3 3 2 |=0+4+6-3-0-6=1≠0| 1 2 1 |∴ X=(A-E)^(-1)A[ 0 2 1 1 2 1 ][ 3 3 2 3 4 2 ] →[ 1 2 1 1 2 2 ]-------------------------------------------[ 1 2 1 1 2 2 ][ 3 3 2 3 4 2 ] →[ 0 2 1 1 2 1 ]------------------------------------[ 1 0 0 0 0 1 ][ 3 3 2 3 4 2 ] →[ 0 2 1 1 2 1 ]------------------------------------------[ 1 0 0 0 0 1 ][ 0 3 2 3 4 -1 ] →[ 0 2 1 1 2 1 ]-----------------------------------------[ 1 0 0 0 0 1 ][ 0 1 1 2 2 -2 ] →[ 0 2 1 1 2 1 ]------------------------------------------[ 1 0 0 0 0 1 ][ 0 1 1 2 2 -2 ] →[ 0 0 1 3 2 -5 ]-----------------------------------[ 1 0 0 0 0 1 ][ 0 1 0 -1 0 3 ] →[ 0 0 1 3 2 -5 ]--------------------------------------[ 0 0 1 ]X= [ -1 0 3 ] [3 2 -5 ]