Find the eigenvalues and eigenvectors of .
I have found the eigenvalues for this problem being and .
My problem is i'm having trouble working out the corrosponding eigenvectors.
To find the eigenvectors, one must find find a basis for the null space. Fortunately, in your case it is really easy because you have distinct eigenvalues, so you only need to find vectors that satisfy .
In layman's terms subtract your eigenvalues from the diagonal and solve the rsystem of equation for x and y when it is set equal to zero.