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

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Q: 3. Let A be a n x n matrix with distinct and positive eigenvalues. For each i, 1 ≤ i ≤n, let Vi be…

A: Given that A be a n×n matrix with distinct and positive eigenvalues. For each i, 1≤i≤n, let vi be an…