AX=2X+A以知a={1-1001-1-101}求x请问用初等变换怎么求?用了好多次行变换没换出来.

Question

AX=2X+A 以知a={ 1 -1 0 0 1 -1 -1 0 1 } 求 x请问用初等变换怎么求?用了好多次行变换没换出来.

Answer 1

因为 AX=2X+A所以 (A-2E)X=A
(A-2E,A)=
-1 -1 0 1 -1 0
0 -1 -1 0 1 -1
-1 0 -1 -1 0 1
r1*(-1),r3+r1
1 1 0 -1 1 0
0 -1 -1 0 1 -1
0 1 -1 -2 1 1
r1+r2,r3+r2,r2*(-1)
1 0 -1 -1 2 -1
0 1 1 0 -1 1
0 0 -2 -2 2 0
r3*(-1/2),r1+r3,r2-r3
1 0 0 0 1 -1
0 1 0 -1 0 1
0 0 1 1 -1 0
X =
0 1 -1
-1 0 1
1 -1 0