设A=
(1-30
210
002)
且A+X=XA,求X
解:由A+X=XA得X(A-E)=A,又|A-E|= |0 -3 0| |2 0 0| |0 0 1| =6≠0,所以A-E可逆,因此X=A(A-E)-1= (1 -3 0 2 1 0 0 0 2) (0 -3 0 2 0 0 0 0 1) = (1 -3 0 2 1 0 0 0 2) (0 1/2 0 -1/3 0 0 0 0 1) = (1 1/2 0 -1/3 1 0 0 0 2)
设A=
(1-30
210
002)
且A+X=XA,求X
解:由A+X=XA得X(A-E)=A,又|A-E|= |0 -3 0| |2 0 0| |0 0 1| =6≠0,所以A-E可逆,因此X=A(A-E)-1= (1 -3 0 2 1 0 0 0 2) (0 -3 0 2 0 0 0 0 1) = (1 -3 0 2 1 0 0 0 2) (0 1/2 0 -1/3 0 0 0 0 1) = (1 1/2 0 -1/3 1 0 0 0 2)