Complex eigenvalues and eigenspace question help

promitheus

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What I'm struggling with on this question is proceeding to find the eigenvector, having found the eigenvalues. I know that I have to reduce the matrix to RREF to derive my eigenvectors, however the eigenvalue is quite intimidating to work with. So I'd like to know if I have made an error, and some/any advice :).
 

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What I'm struggling with on this question is proceeding to find the eigenvector, having found the eigenvalues. I know that I have to reduce the matrix to RREF to derive my eigenvectors, however the eigenvalue is quite intimidating to work with. So I'd like to know if I have made an error, and some/any advice :).
Let y stand for lamda. (-3-y)(3-y) \(\displaystyle \neq\) -(3-y)2
 
Oh my god, thank you. This is why you shouldn't stare at a screen for too long. Totally embarrassed I didn't catch this myself. I've literally spent 2 hours on this thing!
 
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