### Introduction

The power of matrix algebra is seen in the representation of a system of simultaneous linear equations as a matrix equation. Matrix algebra allows us to write the solution of the system using the inverse matrix of the coefficients. In practice the method is suitable only for small systems. Its main use is the theoretical insight into such problems which it provides.

#### Prerequisites

- be familiar with the basic rules of matrix algebra
- be able to evaluate $2\times 2$ and $3\times 3$ determinants
- be able to find the inverse of $2\times 2$ and $3\times 3$ matrices

#### Learning Outcomes

- use the inverse matrix of coefficients to solve a system of two linear simultaneous equations
- use the inverse matrix of coefficients to solve a system of three linear simultaneous equations
- recognise and identify cases where there is no solution or no unique solution

#### Contents

1 Solving a system of two equations using the inverse matrix2 Engineering Example 2

2.1 Currents in two loops

3 Non-unique solutions

4 Solving three equations in three unknowns

4.1 Equations with no unique solution