zonazoo 3 years ago Finding eigenvectors: Can some just show me the steps to find the eigenvector of the following matrix, with (lambda)=2. Matrix is given below.

1. zonazoo

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

2. brinethery

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.

3. zzr0ck3r

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

4. zzr0ck3r

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

5. zzr0ck3r

6. zonazoo

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.

7. zzr0ck3r

o sorry you labda is given

8. zzr0ck3r

you have your lambda its 2

9. zonazoo

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

10. zzr0ck3r

so solve for the null space of that equation

11. zzr0ck3r

one sec

12. zonazoo

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

13. TuringTest

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

14. zzr0ck3r

15. zonazoo

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

16. zzr0ck3r

np