3. Let A be a n x n matrix with distinct and positive eigenvalues. For each i, 1 ≤ i ≤n, let Vi be an eigenvector of A with eigenvalue A, such that the v; are mutually orthogonal unit vectors. That is, Vi · Vj = 1, for i = j, 0, for i #j. (a) Suppose that w = V₁ for some a, E R. Prove that w.v; = a; for all j = 1,..., n. (b) Show that x- (Ax) ≥ 0 for all x ER".

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