Let V be a vector space of dimension 4, and let W be a vector space of dimension 2. Let L : V → W be a linear transformation such that L(V) = W. Determine whether or not the following statement is true: If E is a basis for the vector space V, then two elements of E are in the kernel of L and two elements of E are not in the kernel of L. If the statement is true, prove it. If the statement is false, provide an example showing that it is false. Be sure to explain all of your reasoning.

Let V be a vector space of dimension 4, and let W be a vector space of dimension 2. Let L : V → W be a linear transformation such that L(V) = W. Determine whether or not the following statement is true: If E is a basis for the vector space V, then two elements of E are in the kernel of L and two elements of E are not in the kernel of L. If the statement is true, prove it. If the statement is false, provide an example showing that it is false. Be sure to explain all of your reasoning.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.4: Linear Transformations

Problem 24EQ

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