Calculate Eigen Vector And Eigen Value

Question

This matrix is singular with rank one. Find three $λ$’s and three eigenvectors.

$\begin{bmatrix}1\\2 \\1 \end{bmatrix}$ $\begin{bmatrix}2&1 &2 \end{bmatrix}$ =  $\begin{bmatrix}2 & 1 &2\\4 & 2 & 4\\2 & 1 &2\end{bmatrix}$

Answer 1

λ= 0,0,6 and respective eigen_vectors are,

[k1,  k2,  -k1-k2/2],  [k1,  k2,  -k1-k2/2],  k[1, 2, 1].........

where k1, k2 and k are arbitrary constants..

Comments

I am getting.

for lamnda = 0

eigen vectors are = [-1, 2, 0] and [-1,0, 1]

and for lambda = 6

E.vector is [1, 2, 1]

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yes, your answer is correct, but you are taking particular solution..

i have taken general solution in term of arbitrary constants...

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@Joshi_Nitish ,I think for  λ= 0 , Eigen vector  should be [k₁,  k₂,  (-2k₁-k₂)/2] ..

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(-2k₁-k₂)/2 = -k₁-k₂/2 

isn't it?

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ohh sorry.. I read it wrong..