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A2. Let v be a fixed vector in an inner product space V. Let W be...

A2. Let v be a fixed vector in an inner product space V. Let W be the subset of V consisting of all vectors in V that are orthogonal to v. In set language, W = { w LaTeX: \in
∈V: <w, v> = 0}. Show that W is a subspace of V. Then, if V = R3, v = (1, 1, 1), and the inner product is the usual dot product, find a basis for W.

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