Question: Let W be a subspace of R n and v a vector in R n . Suppose that w and w are orthogonal vectors with

Let W be a subspace of Rⁿ and v a vector in Rⁿ. Suppose that w and w′ are orthogonal vectors with w in W and that 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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