5. Let {u1, u2} be an orthonormal basis for an inner product space V. If r = c u1 +czuz is a vector such that ||a|| = 3 and (r, u2) = 0, then what are the possible values of c and c2? (a) e1 = 2 = V3 (b) c = 3, c2 = 0 (c) c1 = +3, cz =1 (d) c1 = C +3, c2 =0 (e) None of the above 6. What is the value of (1, cos r) in the inner product space C[0, )? (a) 0 (b) 1 (c) 2 (d) 3 (e) None of the above 7. Which of the following maps L: P3 → P2 are linear? (I) L(p(x)) = xp(x) (II) L(p(x)) = r² + p(x) (III) L(p(z)) = p(r) + xp(x) + r?p'(x) (a) Only I (b) Only I and II (c) Only I and III (d) Only II and III (e) I, II, and III

5. Let {u1, u2} be an orthonormal basis for an inner product space V. If r = c u1 +czuz is a vector such that ||a|| = 3 and (r, u2) = 0, then what are the possible values of c and c2? (a) e1 = 2 = V3 (b) c = 3, c2 = 0 (c) c1 = +3, cz =1 (d) c1 = C +3, c2 =0 (e) None of the above 6. What is the value of (1, cos r) in the inner product space C[0, )? (a) 0 (b) 1 (c) 2 (d) 3 (e) None of the above 7. Which of the following maps L: P3 → P2 are linear? (I) L(p(x)) = xp(x) (II) L(p(x)) = r² + p(x) (III) L(p(z)) = p(r) + xp(x) + r?p'(x) (a) Only I (b) Only I and II (c) Only I and III (d) Only II and III (e) I, II, and III

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.3: Orthonormal Bases:gram-schmidt Process

Problem 17E: Complete Example 2 by verifying that {1,x,x2,x3} is an orthonormal basis for P3 with the inner...

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