Suppose that the 2x2 matrix A has only one eigenvalue λ with eigenvector v, and that w is a non zero vector which is not an eigenvector..show that:

a) v and w are linearly independent

b) the matrix with respect to the basis {v, w} is

(λ c

0 λ) for some c =not to 0

c) for a suitable choice of w, c = 1

I am stuck.

I know how to show that eigenvectors are linearly independent, but how do I show that these two vectors are linearly independent to eachother?

as for b and c i dont know where to start! Please help!