Let P, have the inner product given by evaluation at -2, - 1, 1, and 2. Let po (t) = 1, p, (t) = 2t, and p2 (t) = r*. a. Compute the orthogonal projection of p, onto the subspace spanned by Po and p,....

Extracted text: Let P, have the inner product given by evaluation at -2, - 1, 1, and 2. Let po (t) = 1, p, (t) = 2t, and p2 (t) = r*. a. Compute the orthogonal projection of p, onto the subspace spanned by Po and p,. b. Find a polynomial q that is orthogonal to Po and p,, such that (Po.P1.9, is an orthogonal basis for Span(Po P,.P2}. Scale the polynomial q so that its vector of values at (-2, - 1,1,2) is (1, - 1,- 1,1). a. p, =(Simplify your answer.)