Question

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

Matrix is given below.

Answer 1

\[\left[\begin{matrix}-1 & 2 & -1\\ 3 & 0 & 1\\ -3 & -2 & -3\end{matrix}\right]\]

Answer 2

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.

Answer 3

first do A - bI
where b is some constant variable and I is the identity matrix

Answer 4

so
[-1-b,2,-1;3,-b,1;-3,-2,-3-b]

Answer 5

understand? b is your lamda

Answer 6

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.

Answer 7

o sorry you labda is given

Answer 8

you have your lambda its 2

Answer 9

and I have all three eigenvalues, but for some reason when i am calculating for the eigenvector, i am not getting the right answer

Answer 10

so solve for the null space of that equation

Answer 11

one sec

Answer 12

and if i can see how to do it just for lambda = 2 , i can figure out the other two eigenvectors.

Answer 13

if I remember this right, you just plug in each lambda and solve
(A-b_1*I)=0
(A-b_2*I)=0

Answer 14

ahhh, got it, okay... i see where i went wrong, thank you for the help

Answer 15

np