### Introduction

Engineers often need to solve large systems of linear equations; for example in determining the forces in a large framework or finding currents in a complicated electrical circuit. The method of Gauss elimination provides a systematic approach to their solution.

#### Prerequisites

- be familiar with matrix algebra

#### Learning Outcomes

- identify the row operations which allow the reduction of a system of linear equations to upper triangular form
- use back-substitution to solve a system of equations in echelon form
- understand and use the method of Gauss elimination to solve a system of three simultaneous linear equations

#### Contents

1 Solving three equations in three unknowns2 The general system of three simultaneous linear equations

3 Equations which have an infinite number of solutions

4 Engineering Example 3

4.1 Currents in three loops

5 Engineering Example 4

5.1 Velocity of a rocket