Let W be the subspace of R* with an orthonormal basis S = {w,,W2, W3}, where (0, 1, – 1, 0), w, = ¿(1, 1, 1, 1' & w,= }a. -1, -1. 1) T T 1 (0, 1, – 1, 0)", /2 (1, 1, 1, 1) & W3 2 W1 W2 (1, -1, -1, 1) a- Find a basis of W + (the orthogonal complement of W). b- Given V = (-1, 1, 2,1)", write v = u + w, where w is the closest vector to v in W and u is the closest vector to v in W -. c- Which one is closer to v: W or W-? Give reasons.

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