1.F.2 Let B = {1, x, x², x³} be the standard basis of P<3. a) What are the coordinates of 5³ – 2x+1 in the standard basis of P<3? Warning: Don't forget, comes LAST in this ordered basis. b) Use coordinate vectors (in the standard basis) to test the linear independence of {1 – 2x² – r³, x + 2x³, 1+ x – 2x²}. c) Use coordinate vectors (in the standard basis) to test the linear independence of {(x–1)³, (x- 2)², (x – 3)(x² – 8x +11)}.

1.F.2 Let B = {1, x, x², x³} be the standard basis of P<3. a) What are the coordinates of 5³ – 2x+1 in the standard basis of P<3? Warning: Don't forget, comes LAST in this ordered basis. b) Use coordinate vectors (in the standard basis) to test the linear independence of {1 – 2x² – r³, x + 2x³, 1+ x – 2x²}. c) Use coordinate vectors (in the standard basis) to test the linear independence of {(x–1)³, (x- 2)², (x – 3)(x² – 8x +11)}.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.1: Orthogonality In Rn

Problem 7EQ

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