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Finding eigenvectors: Can some just show me the steps to find the eigenvector of the following matrix, with (lambda)=2. Matrix is given below.

Mathematics
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\[\left[\begin{matrix}-1 & 2 & -1\\ 3 & 0 & 1\\ -3 & -2 & -3\end{matrix}\right]\]
I hated linear algebra and don't remember anything, but I will suggest Paul's online notes for these (just Google is). Also, if you can get your hands on a pdf copy of 'Elementary Linear Algebra' by Larson and Falvo.
first do A - bI where b is some constant variable and I is the identity matrix

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Other answers:

so [-1-b,2,-1;3,-b,1;-3,-2,-3-b]
understand? b is your lamda
yes, but I thought you used A-bI=0, in order to find all the lambdas... and then use Ax=bx, in order to find the eigenvectors.
o sorry you labda is given
you have your lambda its 2
and I have all three eigenvalues, but for some reason when i am calculating for the eigenvector, i am not getting the right answer
so solve for the null space of that equation
one sec
and if i can see how to do it just for lambda = 2 , i can figure out the other two eigenvectors.
if I remember this right, you just plug in each lambda and solve (A-b_1*I)=0 (A-b_2*I)=0
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ahhh, got it, okay... i see where i went wrong, thank you for the help
np

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