| 13 Define T: R3 → R2 by T(x, y, z) = (4x + 5y + 6z, 7x +8y + 9z) Suppose o1,02 denotes the dual basis of the standard basis of R2 and V1, 2, V3 denotes the dual basis of the standard basis of R3. Describe the linear functionals T' (@1) and T' (02). (a) Write T'(1) and T'(42) as linear combinations of 1, 2, V3. (b)

| 13 Define T: R3 → R2 by T(x, y, z) = (4x + 5y + 6z, 7x +8y + 9z) Suppose o1,02 denotes the dual basis of the standard basis of R2 and V1, 2, V3 denotes the dual basis of the standard basis of R3. Describe the linear functionals T' (@1) and T' (02). (a) Write T'(1) and T'(42) as linear combinations of 1, 2, V3. (b)

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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