求线性代数解答！！

Answer 1

|A| =
|1 1 -1|
|0 2 0|
|1 -1 1|
= 2*2 = 4
A*X = A^(-1)+ 2X
|A|A^(-1)X = A^(-1) +2X
4A^(-1)X = A^(-1) +2X
4X = E +2AX
(4E-2A)X = E
X = (4E-2A)^(-1) = (1/2)(2E-A)^(-1)
(2E-A, E) =
[ 1 -1 1 1 0 0]
[ 1 1 -1 0 1 0]
[-1 1 1 0 0 1]
行初等变换为
[ 1 -1 1 1 0 0]
[ 0 2 -2 -1 1 0]
[ 0 0 2 1 0 1]
行初等变换为
[ 1 -1 0 1/2 0 -1/2]
[ 0 2 0 0 1 1]
[ 0 0 1 1/2 0 1/2]
行初等变换为
[ 1 0 0 1/2 1/2 0]
[ 0 1 0 0 1/2 1/2]
[ 0 0 1 1/2 0 1/2]
X = (1/2)(2E-A)^(-1) =
[ 1/4 1/4 0]
[ 0 1/4 1/4]
[ 1/4 0 1/4]

Answer 2

A^T*B=
-1 2
-1 3
|A^T*B|=-1
A*=
3 -2
1 -1
(A^T*B)^(-1)=
-3 2
-1 1
线性代数包括行列式、矩阵、线性方程组、向量空间与线性变换、特征值和特征向量、矩阵的对角化，二次型及应用问题等内容。