Let W be a subspace of n and v a vector in n . Suppose that w and w are orthogonal

Chapter 5, Problem 5.2.25

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Let W be a subspace of n and v a vector in n . Suppose that w and w are orthogonal vectors with w in W and hat v w w. Is it necessarily true that w is in W?Either prove that it is true or find a counterexample.

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