求特征值和全部特征向量

来源：百度知道 编辑：UC知道 时间：2024/05/07 02:19:09
要完整的步骤，谢谢各位了~

求特征值和全部特征向量

-1 1 0
A=-4 3 0
1 0 2

f(λ)=（λ-1)(λ-1)(λ+1)
So λ=1 or -1
When λ=1:
Compute the equation system [E-A]X=O;
we get X=(-1,-2,1)'
so the eigenvector belonging to λ=1 is
ζ1=-ε1-2ε2+ε3
When λ=-1
Compute the equation system [-E-A]X=O
we get X=(1,1,1)'
So the eigenvector belonging to λ=-1 is
ζ2=ε1-ε2+ε3