4. Consider the linear map f : R1[X] → R1[X] given by f(ao + a1X) = (2ao +3a1)+ (ao – a1)X. Find the standard matrix Af corresponding to this linear map relative to the standard basis of R1 X]. Is f an isomorphism of vector spaces? Justify your answer.

4. Consider the linear map f : R1[X] → R1[X] given by f(ao + a1X) = (2ao +3a1)+ (ao – a1)X. Find the standard matrix Af corresponding to this linear map relative to the standard basis of R1 X]. Is f an isomorphism of vector spaces? Justify your answer.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.6: Introduction To Linear Transformations

Problem 55EQ

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4. Consider the linear map f : R1[X] → R1[X] given by
f(ao+ a1X) = (2a0 +3a1)+ (ao – a1)X.
%3D
Find the standard matrix Af corresponding to this linear map relative to the standard basis of R1 X].
Is f an isomorphism of vector spaces? Justify your answer.

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