Question: 7. Let WI = , W2 = , W3 = , W4 = and S = {w1, w2, w3, WA}. You may take for granted

7. Let WI = , W2 = , W3 = , W4 = and S = {w1, w2, w3, WA}. You may take for granted that S is linearly independent. (a) Apply Gram-Schmidt orthogonalization to construct an orthogonal basis { v1, v2, v3, VA} for (S), for which wj is a linear combination of v1, ..., V; for each j = 1, 2,3, 1. (b) Let z be a vector in 125. Show that z is a vector in (S) if and only if z = (z, VI) (Z, V2) (Z, V3) (Z, VA) lv 2 V1 1/V 2 / / 2 V2 + 1/ V 3 1/2 V3 + V4. (c) Let U = , u i. Compute (u, v;), (u', v;), and I/vil|2 for each j = 1, 2, 3, 1. ii. Does u belong to (S)? Justify your answer. iii. Does u' belong to (S)? Justify your

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