- #1
jjones1573
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Homework Statement
Im looking at finding the eigenvectors of a matrix but also a basis for the eigenspace
A = [ 6 16 ]
[ -1 -4 ]
lambda = 4
lambda = -2
Homework Equations
(A - lambda I ) v = 0
The Attempt at a Solution
So with the above equation I get:
for lambda = 4
[ 6 - 4 16 ] [ v1 ] = [ 0 ]
[ -1 -4 - 4 ] [ v2 ] [ 0 ]
so
2 v1 + 16 v2 = 0
-v1 - 8v2 = 0
so v1 = 8v2
and the basis for the eigenspace is span [ 8 ]
[ 1 ]
First is that right? because when I put it into an eigenvector calculator on the web it gives me
-8 instead of 8 but I can't see how I could get to that.
Second if this is the basis for the eigenspace then how can I find the eigenvectors for the eigenvalue?
thanks,