Let set of prime numbers P 3 have the inner product given by evaluation at minus 2, minus 1, 1, and 2 . Let p 0 (t )equals1, p 1 (t )equalst, and p 2 (t )equalst Superscript 4 . a. Compute the orthogonal projection of p 2 onto the subspace spanned by p 0 and p 1 . b. Find a polynomial q that is orthogonal to p 0 and p 1 , such that StartSet p 0 comma p 1 comma q EndSet is an orthogonal basis for Span StartSet p 0 comma p 1 comma p 2 EndSet . Scale the polynomial q so that its vector of values at (negative 2 comma negative 1 comma 1 comma 2 )is (1 comma negative 1 comma negative 1 comma 1 ).
