### Introduction

When we wish to solve large systems of simultaneous linear equations, which arise for example in the problem of finding the forces on members of a large framed structure, we can isolate the coefficients of the variables as a block of numbers called a matrix. There are many other applications matrices. In this Section we develop the terminology and basic properties of a matrix.

#### Prerequisites

- be familiar with the rules of number algebra

#### Learning Outcomes

- express a system of linear equations in matrix form
- recognise and use the basic terminology associated with matrices
- carry out addition and subtraction with two given matrices or state that the operation is not possible

#### Contents

1 Applications of matrices1.1 Representing simultaneous linear equations

1.2 Representing networks

2 Definitions

2.1 Square matrices

2.2 Some examples of matrices and their classification

2.3 Equality of matrices

2.4 The unit matrix

2.5 The zero matrix

2.6 The transpose of a matrix

3 Addition and subtraction of matrices

4 Multiplication of a matrix by a number

5 Some simple matrix properties