Question

线性代数问题求解答

Answer 1

有帮助请采纳呦～

Answer 2

|λE - A| =
|λ-17 2 2|
| 2 λ-14 4|
| 2 4 λ-14|
|λE - A| =
|λ-17 2 2|
| 0 λ-18 18-λ|
| 2 4 λ-14|
|λE - A| =
|λ-17 2 4|
| 0 λ-18 0|
| 2 4 λ-10|
= (λ-18) [(λ-17) (λ-10) - 8]
= (λ-9)(λ-18)^2
特征值 矩阵 λ = 9, 18, 18
对于特征值λ= 9，λE - A =
[-8 2 2]
[ 2 -5 4]
[ 2 4 -5]
初等行变换为
[ 2 -5 4]
[ 0 9 -9]
[ 0 -18 18]
初等行变换为
[ 2 0 -1]
[ 0 1 -1]
[ 0 0 0]
得特征向量 (1, 2, 2)^T,
对于重特征值 λ=18，λE - A =
[1 2 2]
[2 4 4]
[2 4 4]
初等行变换为
[ 1 2 2]
[ 0 0 0]
[ 0 0 0]
得特征向量 (2, -1, 0)^T, (2, 0, -1)^T