|Nov20-08, 10:39 PM||#1|
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:
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
|Nov20-08, 11:00 PM||#2|
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?
|Nov20-08, 11:12 PM||#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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