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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 cant 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,