Introduction

Introduction

In Class 10 you solved a pair of simultaneous linear equations in two unknowns using a determinant of order two. This chapter extends that idea to determinants of order three, which are the natural tool for solving three simultaneous linear equations in three unknowns, and which show up repeatedly in engineering and economic modelling.

Historically, the idea of a determinant is credited to the German mathematician G. W. Leibnitz (1676–1714), and it was Gabriel Cramer (1750) who developed the systematic rule — now called Cramer's Rule — for using determinants to solve systems of linear equations. We will build up to that rule later in the chapter (§4.3.1), after first mastering how a determinant of order two and order three is written, expanded, and manipulated.

The second half of the chapter turns to matrices — rectangular arrangements of numbers — which generalise the square arrangement of a determinant to any number of rows and columns, and which have their own algebra of addition, scalar multiplication and multiplication.