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Let V be an inner product space. Prove that if w⃗ is orthogonal to each of...

Let V be an inner product space. Prove that if w⃗ is orthogonal to each of the vectors in the set

S = {⃗v1, ⃗v2, . . . , ⃗vm}, then w⃗ is also orthogonal to each of the vectors in the subspace W = SpanS of V .

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