### Introduction

In this Section we will reconsider the Gaussian elimination approach discussed in
**
HELM booklet
**
8, and we will see how rounding error can grow if we are not careful in our implementation of the approach. A method called partial pivoting, which helps stop rounding error from growing, will be introduced.

#### Prerequisites

- revise matrices, especially matrix solution of equations
- recall Gaussian elimination
- be able to find the inverse of a $2\times 2$ matrix

#### Learning Outcomes

- carry out Gaussian elimination with partial pivoting

#### Contents

1 Gaussian elimination2 Partial pivoting

2.1 An example to motivate the idea

2.2 Partial pivoting in general