) Suppose L : V → W is a linear transformation such that the kernel of L is trivial, that is, ker(L) = {0}. Prove that L is one-to-one. (use the definitions) Hint: Start with L(v1) − L(v2) = 0 and use linearity of L. (b) Prove the converse of (a), that is, suppose L : V → W is a one-to-one linear transformation and prove that ker(L) = {0}. (use the definitions) Hint: Start with v ∈ ker(L) and use the

) Suppose L : V → W is a linear transformation such that the kernel of L is trivial, that is, ker(L) = {0}. Prove that L is one-to-one. (use the definitions) Hint: Start with L(v1) − L(v2) = 0 and use linearity of L. (b) Prove the converse of (a), that is, suppose L : V → W is a one-to-one linear transformation and prove that ker(L) = {0}. (use the definitions) Hint: Start with v ∈ ker(L) and use the

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 4EQ

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