7. This problem requires calculus. Let P = {a,x" + an–1x"-1 + ...+ a1x + ao | n > 0, ao, . ., an E R} be the set of all polynomials with real coefficients. Let F :P → P by, for all pE P, F(p) = p', where p' is the derivative of p. (a) Find F(3x5 - 2² + x). (b) Find p e P such that F(p) = x³ + 5x² – 4. Is p unique? (c) Find ran F and prove your answer is correct. 7,2

7. This problem requires calculus. Let P = {a,x" + an–1x"-1 + ...+ a1x + ao | n > 0, ao, . ., an E R} be the set of all polynomials with real coefficients. Let F :P → P by, for all pE P, F(p) = p', where p' is the derivative of p. (a) Find F(3x5 - 2² + x). (b) Find p e P such that F(p) = x³ + 5x² – 4. Is p unique? (c) Find ran F and prove your answer is correct. 7,2

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.5: The Kernel And Range Of A Linear Transformation

Problem 30EQ

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