Let S = {VI. V2 ..... \'l l be an orthononnal baSIS for the Euclidean space V and 1(/ 1. (12.' '" ad be any itt of scal3rs none of which is zero. Prove th3t is an onhogonal basis for V. How should Ihe scalars al' a2 . .... til be chosen so thaI T is an onhononlJaI basis for V'?

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