solve #5 please, Show all of your work on pictures and explain each step you make.Thank you! 5. Let T: P₂ (R) → P₂(R) be defined as P(ax² +bx+c)=( (2a − b)x² + (3a + 3c)x + (a − 2b -3c)). Find Ker(T) and Rng(T). Is T an isomorphism? How do you know? If T is an isomorphism,find the inverse of T.6. Let

5. Given that T:P2ℝ→P2ℝ be defined as Tax2+bx+c=2a-bx2+3a+3cx+a-2b-3c. We have to find the KerT and…

Answered: 5. Let T: P₂ (R) → P₂ (R) be defined as…

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 27EQ

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5. Let T: P₂ (R) → P₂ (R) be defined as P(ax² +bx+c)=((2a − b)x² + (3a + 3c)x+ (a − 2b - 3c)). Find Ker(T) and Rng(T). Is T an isomorphism? How do you know? If T is an isomorphism, find the inverse of T.