## Finding basis for an eigenspace

1. The problem statement, all variables and given/known data
Find a basis and dimension for each eigenspace of the matrix:

4 2
3 3

2. Relevant equations

3. 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

 PhysOrg.com science news on PhysOrg.com >> Front-row seats to climate change>> Attacking MRSA with metals from antibacterial clays>> New formula invented for microscope viewing, substitutes for federally controlled drug
 Recognitions: Homework Help Science Advisor 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?
 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