Let set of prime numbers P 3ℙ3 have the inner product given by evaluation at minus−22, minus−1, 1, and 22. Let p 0 (t )p0(t)equals=1, p 1 (t )p1(t)equals=2 t2t, and p 2 (t )p2(t)equals=t Superscript 6t6. a. Compute the orthogonal projection of p 2p2 onto the subspace spanned by p 0p0 and p 1p1. b. Find a polynomial q that is orthogonal to p 0p0 and p 1p1, such that StartSet p 0 comma p 1 comma q EndSetp0,p1,q is an orthogonal basis for Span StartSet p 0 comma p 1 comma p 2 EndSetSpanp0,p1,p2. Scale the polynomial q so that its vector of values at (negative 2 comma negative 1 comma 1 comma 2 )(−2,−1,1,2) is (1 comma negative 1 comma negative 1 comma 1 )(1,−1,−1,1). Let P, have the inner product given by evaluation at -2, -1, 1, and 2. Let po(t) = 1, P,(t) = 2t, and po(t) = tº
a. Compute the orthogonal projection of P2 onto the subspace spanned by Po and P1
b. Find a polynomial that is orthogonal to P, and p,, such that (po pr.) is an orthogonal basis for Span{p. P.p . Scale the polynomial q so that its vector of values at (-2,-1,1,2) is (1,-1,-1,1).
a. P2 =
b. q =