线性代数题,for what value of x,if any,will the matrix（是否存在X使得该矩阵）

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/22 00:21:39

线性代数题,
for what value of x,if any,will the matrix（是否存在X使得该矩阵）
[ 3 0 0]
A=[ 0 x 2]
[0 2 x]
have at least one repeated eigenvalue?（拥有至少一个重复特征值）

我用b代替 lamda
| A - bE| = (3-b)(x+2-b)(x-2-b)
所以A的特征值为 :3,x+2,x -2
若有重复的特征值,必有 x+2 =3 或 x-2 = 3 ( x+2 = x -2 不可能.)
即 x = 1 或 x = 5 时有重复的特征值 3.

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