There are three vectors in R4 that are linearly independent but not orthogonal: u = (3,...

There are three vectors in R4 that are linearly independent but not orthogonal: u = (3, -1, 2, 4), v = (-2, 7, 3, 1), and w = (-3, 2, 4, 11). Let W = span {u, v, w}. In addition, vector b = (2, 1, 5, 4) is not in the span of the vectors. Compute the orthogonal projection bˆ 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' , v' , w'} 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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If you have any doubts in the solution please ask me in comment it is a huge calculation ....

Colby Messinger answered 1 year ago

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