Problem 4. (a) Let m, nЄ N. Prove that for any linear transformation T: R→ Rm, there is an orthonormal basis (un) of R" such that for all 1 ≤ i, j ≤ n, if i j then T() T(u) = 0. (Hint: use the Spectral Theorem, 8.1.1 in the text). (b) Let T: R³ → R² be the linear transformation defined by T() = A for all 7 € R³, where A = 3 2 2 23-2 (1, 2, 3) of R³ as in part (a) above, i.e., satisfying Find an orthonormal basis u = T(u).T(ū2) = T(1) T(3) = T(2) · T(3) T(2).T(3) = 0.