3. Consider the basis S = {1, x, x²} in the vector space P2, the set of all polynomials of degree at most 2, where P2 is a subspace of L²[0, 1]. (a) Show that S = {1, x, x²} is not an orthogonal set in L²[0, 1]. (b) Use the Gram-Schmidt algorithm to generate an orthonormal basis E S. = {e1, e2, e3} from (c) Use E to find the polynomial p = p(x) of degree at most 2 that best approximates f(x) = { 2, 1/2 x ≤1 0, 0≤x≤1/2 (i.e., find the (orthogonal) projection of f onto the space P₂ spanned by E). (d) Sketch p and f on the same set of axes.