Linear Algebra: A Modern Introduction

Published by Cengage Learning
ISBN 10: 1285463242
ISBN 13: 978-1-28546-324-7

Chapter 1 - Vectors - 1.1 The Geometry and Algebra of Vectors - Exercises 1.1: 37

Answer

$\mathbb{Z}_3$: $2$ $\mathbb{Z}_4$: $0$ $\mathbb{Z}_5$: $3$.

Work Step by Step

First perform the computation in $\mathbb{Z}$: $$2+1+2+2+1=8$$ The result of the computation in $\mathbb{Z}_n$ is the remainder of $8$ divided by $n$. So in $\mathbb{Z}_3$, the result is $2$; in $\mathbb{Z}_4$, $0$; and in $\mathbb{Z}_5$, $3$.
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