Part 1: Pick any three vectors u, v, w in R 4 which are linearly independent but not orthogonal and a vector b which is not in the span of u, v, w. If any of your vectors u, v, w are scalars of the standard basis vectors e1, e2, e3, e4 then start over. Let W = span{u, v, w}. Compute the orthogonal projection ˆb of b onto the subspace W in two ways: (1) using the basis {u, v, w} for W, and (2) using an orthogonal basis {u 0 , v0 , w0} obtained from {u, v, w} via the Gram-Schmidt process. Finally, explain in a few words why the two answers differ, and explain why only ONE answer is correct.

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