Question

高等数学第(2)题求解。

Answer 1

AX=2X+A, (A-2E)X=A, X=(A-2E)^(-1)*A
(A-2E, E) =
[-1 -1 0 1 0 0]
[ 0 -1 -1 0 1 0]
[-1 0 -1 0 0 1]
行初等变换为
[1 1 0 -1 0 0]
[0 1 1 0 -1 0]
[0 1 -1 -1 0 1]
行初等变换为
[1 1 0 -1 0 0]
[0 1 1 0 -1 0]
[0 0 -2 -1 1 1]
行初等变换为
[1 1 0 -1 0 0]
[0 1 0 -1/2 -1/2 1/2]
[0 0 1 1/2 -1/2 -1/2]
行初等变换为
[1 0 0 -1/2 1/2 -1/2]
[0 1 0 -1/2 -1/2 1/2]
[0 0 1 1/2 -1/2 -1/2]
则 (A-2E)^(-1) =
[-1/2 1/2 -1/2]
[-1/2 -1/2 1/2]
[ 1/2 -1/2 -1/2]
得 X =
[0 1 -1]
[-1 0 1]
[1 -1 0]

Answer 2

等式两边先同时右乘x的逆，在同时右乘x，就能算出来了

追问

具体

追答

懒得算，