Let P ₃ have the inner product given by evaluation at 3, 1, 1, and 3. Let po(t) = 2, p₁ (t) = t and q(t) = t²-5/4, Notice that these polynomials form an orthogonal set with this inner product. Find the best approximation to p(t) = 3t³ by polynomials in Span (Po,P1.9.
The best approximation to p(t) = 3t³ by polynomials in Span (P₀.P₁,q) is