Recall that two vectors v and w are linearly independent if the only solution to the vector equation av+ bw= 0

is the solution a = b = 0.

Letvandwbe eigenvectors of a matrix M with corresponding nonzero eigenvalues λ and µ such that λ ≠ µ.

(i) Given scalars a and b, ﬁnd an expression for, M(av+ bw), that does not contain M.

(ii) Hence or otherwise, prove that the eigenvectorsvandwmust be linearly independent.

Thanks