Question

线性代数题10求矩阵A=3 1 0(1 3 0)0 0 2的特征值及特征向量!

Answer 1

|λE-A|= |λ-3 -1 0 |

|-1 λ-3 0 |

|0 0 λ-2 |

=(λ-3)^2(λ-2)-(λ-2)

=(λ-2)(λ^2-6λ+8)

=(λ-2)^2(λ-4)

特征值：2 2 4

λ=2

-1 -1 0 x1

-1 -1 0 x2 =0

0 0 0 x3

1 1 0 x1 = 0

x2

x3

λ=2 对应线性无关特征向量有2个：

(-1 1 0)T (0 0 1)T

λ=4

1 -1 0

-1 1 0

0 0 2

λ=4对应线性无关特征向量有1个

(1 1 0)T