Show that the following does not define an inner product on :

Define an inner product on by

Let be the subspace spanned by { }.

(i) Find an orthornormal basis for U.

(ii) Find the polynomial in U that is as close as possible to 1. (for the norm corresponding to the above inner product)

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And a little vector space question,

Determine whether the polynomial

belongs to span { } where

Thanks for your help guys. (: