Let W be a subspace of Rn and v a vector in Rn. Suppose that wand w' are orthogonal vectors with w in W and that v = w+w'. Is it necessarily true that w' is in W 1? Either prove this or show a counterexample. 3. Let {v1, . . vn} be an orthonormal basis for Rn and x in Rn. Show that ||x||2 = |v1 x12+ | vn x/2

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