Please help with both parts b and c:(will leave a like) (b) Show that the function : Z12 → Z12 defined by (a) = a +a is a homomorphism.(c) Find the kernel of the homomorphism : Z12 → Z12 defined by (a) = a + a.

We know that a mapping ϕ:G, ∘→G', ∆ is a homomorphism if for all a, b∈G, we have, the property…

Answered: (b) Show that the function : Z12 → Z12…

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 7EQ

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(b) Show that the function : Z12 → Z12 defined by (a) = a + a is a homomorphism. (c) Find the kernel of the homomorphism : Z12 → Z12 defined by (a) = a + a.