## 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: 49

#### Answer

$x={2}$.

#### Work Step by Step

The elements of $\;\mathbb{Z}_{5}\;$ is 0,1,2,3,4 So, if there is a solution for this equation, then x is one of these numbers. $If \;\;x=0\\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;3.(0)=4 \;\;\; {\color{Red}\rightarrow } \;\;\;\;\;\; 0\neq 4\\ so \;\;0 \;is \;not \;solution\\\\ If \;x=1\\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;3.(1)=4\;\; {\color{Red}\rightarrow } \;\;\; 3\neq 4\\ so\; 1\; is\; not\; solution.\\\\ If\;x=2\\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;3.(2)=4 \;\;\;\;{\color{Red}\rightarrow }\;\;\;\; 1= 1\\ so\; 2\; is\; a \ solution\\\\ If \;x=3\\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;3.(3)=4 \;\;\;{\color{Red}\rightarrow } \;\;\;\; 4\neq 1\\ so\; 2\; is\; not\; solution\\\\ If\; x=4\\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;3.(4)=4 \;\;\;{\color{Red}\rightarrow } \;\;\;2\neq 1\\ so\; 4 \;is\; not\; solution\\\\$ $\;\;\;\;\;\;\;\;\;\;\;\;\;\;x=2$

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