Question

求矩阵特征值,1 2 3 A=2 1 3 3 3 6

Answer 1

|A-λE| = λ(9-λ)(1+λ).
1-λ 2 3
2 1-λ 3
3 3 6-λ
r1-r2
-1-λ 1+λ 0
2 1-λ 3
3 3 6-λ
c2+c1
-1-λ 0 0
2 3-λ 3
3 6 6-λ
= (-1-λ)[(3-λ)(6-λ)-18]
= (-1-λ)[λ^2-9λ]
= λ(9-λ)(1+λ)
所以A的特征值为 0,9,-1