Question: Suppose that V C Rn is a proper subspace, and u1........un, forms an orthonormal basis of V. Prove that there exist vectors um+1,... , un

Suppose that V C Rn is a proper subspace, and u1........un, forms an orthonormal basis of V. Prove that there exist vectors um+1,... , un ∊ R" \ V such that the complete collection u1,... ,un forms an orthonormal basis for Rn.

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