Finding basis for an eigenspace

[DWill]

Homework Statement

Find a basis and dimension for each eigenspace of the matrix:

4 2
3 3

Homework Equations

The Attempt at a Solution

I found the eigenvalues lambda = 1, 6. When trying to find the eigenspace for lambda = 1, I try to solve for x and y here:

|-3 -2| |x| = |0|
|-3 -2| |y| = |0|

I'm not sure how to do the matrix notation on here but I hope it is clear enough. Since I get the same equation twice in the system of equations, is this the right basis: span(-2/3, 1)?

edit: can someone also see if I did the basis for the 2nd eigenvalue (lambda = 6) correctly? I get the basis to be span(1, 1).
So each has dimension of 1

 

[Dick]

Um, yes. If I'm reading your notation correctly, you have the right eigenspace for both. Is this a question, or just a homework check?

 

[DWill]

It was originally going to be a question but I kind of figured it out as I was typing it :)
So I was just making sure.
Thanks