## Linear Algebra: A Modern Introduction

Published by Cengage Learning

# Chapter 1 - Vectors - 1.1 The Geometry and Algebra of Vectors - Exercises 1.1 - Page 17: 31

#### Answer

$$0$$

#### Work Step by Step

We want to find $2+2+2$ in $\mathbb{Z}_3$. Since addition is associative, $2+2+2=(2+2)+2$. In $\mathbb{Z}_3$, $2+2=1$, yielding $2+2+2=1+2$, which, again performing addition, yields $1+2=0$.

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