This is a revision problem I have come across,(adsbygoogle = window.adsbygoogle || []).push({});

I have completed the first few parts of it, but this is the last section and it seems entirely unrelated to the rest of the problem, and I can't get my head around it!

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 the eigenvalues 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!

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# 2x2 matrix A has only one eigenvalue λ with eigenvector v

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