how do i find the eigenvector?

Question

anonymous · Answer

$$\left( A-\lambda I \right)x=0$$lamda is the eigenvalue, x is the eigenvector

anonymous · Answer

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?

myininaya · Answer

@nightshade please don't post off-topic answers.
@exraven and elica85 we want x to not be the zero vector also

myininaya · Answer

Did you try to plug into exraven's formula to find the eigenvectors

anonymous · Answer

i thought it's lambdaI-A, not A-lambdaI

anonymous · Answer

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

anonymous · Answer

o if i just have to find x, i should be able to...

myininaya · Answer

$$(A-\lambda_n \cdot I)x=0$$
For $$\lambda_1=-4$$
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