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Homework Help: Finding basis for an eigenspace

  1. Nov 20, 2008 #1
    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
  2. jcsd
  3. Nov 20, 2008 #2


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    Science Advisor
    Homework Helper

    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?
  4. Nov 20, 2008 #3
    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.
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