1. (5 points) Consider the vector space P2 with inner product (p, q) = Lil p(x)q(x)dx, find the following for 190:) = x2 + 1 and q(x) = 2x2 x: a. (19.61) b. III)\" C. In this Inner Product space (P2 with given inner product), are p(x) = x + 2 and (10:) = x 2 orthogonal? Verify your answer with the appropriate calculation and briefly explain. 2. (5 points) Consider the vector space of all continuous functions on [ 1t, 11'] with the inner product given by (f, g) = f;f(x)g(x)dx. Is the set {1, cos x, sin 3:} is orthogonal? Verify your answer with the appropriate calculation and briefly explain. 3. (5 points) Let R3 have the Euclidean Inner Product. Use the Gram-Schmidt process to transform {(1,1,1), (3,7, 2), (0,4,1)} into an orthonormal basis for R3. 4. (5 points) Repeat question 3 using the inner product (if, 1?) = 111121 + 2112172 + 2113123