# Math Help - Eigenvectors

1. ## Eigenvectors

I wasn't really sure where to put this but here seems the most appropriate place.

I have to find eigenvectors corresponding to the eigenvalues of 0 1 and 4 for the following matrix:

0 -8 4
1 3 -1
2 -2 2

I have already found the eigenvevtors corresponding to 0 and 4, but when lamba =1 there is difficulty. Nothing seems to work when i try to equate the values. What is the way around this?

By the way, when lamba=1, the result is as follows:

-1 -8 4 = 0
1 2 -1 = 0
2 -3 1 = 0

2. What is the problem?

You can simplify the system to:
(By adding the last row to the middle-row)

-x-8y+4z = 0
3x = 0
2x -2y+z = 0

It follows that x = 0, and we can write the system as:

x= 0,
-8y+4z = 0
-2y+z = 0

Last 2 eqations are equivalent and we get: x=0, z = 2y so v=(0,1,2)
Is an eigenvector by lambda= 1

(I see in the last row you put a -3 for the second entry: this must be a -2)

3. Thanks for spotting my mistake. The -3 is the reason i came into difficulty then. I shouldn't have any more problems now.