Finding eigenvectors of a 2x2 matrix
say you have the matrix:
A = (k, 1
now i found the eigenvalues to be k and 2.
im trying to find the eigenvector for the eigenvalue k.
i thought its supposed to work when i do the following...
so if i use (A-lambda(I))v = 0, the matrix reduces to:
(k-k , 1
so v2 = 0 and (2-k)v2 = 0
and we know v1 = 0...
but that means the eigenvector is (0,0) !! how is this possible?
because when i try working out the other way...
so back to our matrix A..
I do Av = lambda(v)
kv1 + v2 = kv1
2v2 = kv2
and i get eigenvector (1,0) which is correct..
so why does the first method not work?? i thought we can use any of those methods....(Doh)