### Introduction

In this Section we consider another direct method for obtaining the solution of systems of equations in the form $AX=B$ .

#### Prerequisites

• revise matrices and their use in systems of equations
• revise determinants

#### Learning Outcomes

• find an $LU$ decomposition of simple matrices and apply it to solve systems of equations
• determine when an $LU$ decomposition is unavailable and when it is possible to circumvent the problem

3.1 Why not?