### Introduction

Among other uses, determinants allow us to
**
determine
**
whether a system of linear equations has a unique solution or not. The evaluation of a determinant is a key skill in engineering mathematics and this Section concentrates on the evaluation of small size determinants. For evaluating larger sizes we can often use some properties of determinants to help simplify the task.

#### Prerequisites

- know what a matrix is

#### Learning Outcomes

- evaluate a $2\times 2$ determinant
- use the method of expansion along the top row to evaluate a determinant
- use the properties of determinants to aid their evaluation

#### Contents

1 Determinant of a 2 $\times $ 2 matrix2 Laplace expansion along the top row

3 Properties of determinants