2) Let V = P5(Q) the vector space consisting of polynomials in the variable x of degree at most 5. Let o E L(V) be a linear map defined by o(f) = x²f" – 6xf' + 12f for any f E V. (a) Prove that p is a linear transformation. (b) Determine a basis for the image and nullspace of q.

2) Let V = P5(Q) the vector space consisting of polynomials in the variable x of degree at most 5. Let o E L(V) be a linear map defined by o(f) = x²f" – 6xf' + 12f for any f E V. (a) Prove that p is a linear transformation. (b) Determine a basis for the image and nullspace of q.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.4: Linear Transformations

Problem 12EQ

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Some help with linear transformation and nullspace and basis

2) Let V = P5(Q) the vector space consisting of polynomials in the variable x of degree at most 5.
Let o E L(V) be a linear map defined by p(f) = x²f" – 6xf' + 12f for any f E V.
(a) Prove that o is a linear transformation.
(b) Determine a basis for the image and nullspace of o.

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