4 -1 -1 0 0 0 0 0 0 (X1 X2 X3 )^T 特征向量基础解系怎么求的

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4 -1 -1 0 0 0 0 0 0 (X1 X2 X3 )^T 特征向量基础解系怎么求的

令A如下
4 -1 -1
0 0 0
0 0 0
则|xE-A|=
x-4 1 1
0 x 0
0 0 x
= (x-4)x²
得到x=4 x=0 x=0
代入得到 三个
(1,0,0) (1,0,4),(1,4,0)

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