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how do i find the eigenvector?

Mathematics
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\[\left( A-\lambda I \right)x=0\]lamda is the eigenvalue, x is the eigenvector
i was able to find the eigenvalue \[\left[\begin{matrix}-6 & 1 \\ -2 & -3\end{matrix}\right]\] to be \[\lambda _{1}=-4, \lambda _{2}=-5\] now what's the next step?
@nightshade please don't post off-topic answers. @exraven and elica85 we want x to not be the zero vector also

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Other answers:

Did you try to plug into exraven's formula to find the eigenvectors
i thought it's lambdaI-A, not A-lambdaI
idk what i'm doing, my school doesn't require us to take linear algebra to take diff eq so i'm suppose to know what to do but i don't
o if i just have to find x, i should be able to...
\[(A-\lambda_n \cdot I)x=0\] For \[\lambda_1=-4\] |dw:1333932816786:dw|
For \[\lambda_2=-5\] |dw:1333932896865:dw|

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