Give .933 the inner product (1106) a (106)) = P(-1)q(-1) + p(0)q(0) + P(1)q(1) + p(2)q(2) and let W= {P(x)6933 | p'(0)=0}, which is a subspace of .953 with basis { q1(x), q2(x), q3(x) }, where (1106) = 1, (1206) = x2, 97306) = x3 (a) (6 marks) Apply the Gram-Schmidt process to { q1(x), q2(x), q3(x) } to find an orthogonal basis { pl(x), p2(x), p3(x) } for W with respect to the given inner product. Choose p1(x), p2(x), p3(x) to all be monic (that is, so that the coefficient on the highest power of x is 1). Show you work. Do not use part (b) below. (b) (5 marks) In part (a), you should have found that x +x Doll- P1(x)=1a p206) = - + x , 9306) = Find projW r(x), where r(x) = x + x3. (The significance of projW r(x) is that it is the unique polynomial p(x) e W with minimal 2 distance to r(x), that is, that minimizes 2 (r(k) p(k))2.) k=1