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8. (a) For what values of a, b, and c can the matrix A below be diagonalized? 2 marks 0 a 1 0 =10 0 0 c b) Let A be an n xn matrix. In class, we showed that if R admits a basis of eigenvectors of A, then there is an invertible atrix P such that P- AP is diagonal (i.e., is zero everywhere apart from along the main diagonal) Show, conversely, that if there exists an invertible matrix P such that P-1AP is diagonal, then R admits a basis of eigenvectors of A. [2 marks

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