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Can anyone explain to me why eigenvector here is like this 
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#1
Mar2914, 05:10 PM

P: 16

Im supposed to find the eigenvectors and eigenvalues of A
I found that eigenvalues are 2 12 and 6 then I found eigen vectors substituting 6 to lambda and someone has told me I get 0 0 1 for eigenvector which I cannot understand why?? can anyone plzzzzzzzzz explain why this is???????? 


#2
Mar2914, 05:23 PM

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P: 12,037

Did you multiply this vector with your matrix? What do you get?
Does this fit to the definition of an eigenvector? 


#3
Mar2914, 05:32 PM

P: 16

it doesn't fit with the definition of eigenvectors so does that mean it should be 0 0 0 instead of 0 0 1?? I mean when you try to calculate for v3 = [ v1 v2 v3] since the last row of the matrix is 0 0 0 should v3 come out as 0?? couldn't v3 be any number?? 


#4
Mar3014, 01:34 AM

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P: 21,397

Can anyone explain to me why eigenvector here is like this
The matrix you showed in the second attachment is not A. It is [A  (6)I]. Of course if you multiply this matrix times your eigenvector, you'll get the zero vector. The kernel here should not consist of only the zero vector  an eigenvector cannot be the zero vector. 


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