ABSTRACT

This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book provides an opportunity to introduce vectors, matrices and determinants. It begins by a brief introduction to coordinate geometry, which illustrates the use of vectors and matrices, and introduces the notion of a linear mapping. The book explains normal forms of matrices, and outlines an important topic with many applications in both algebra and analysis. To solve a system of linear equations means to find all the values of the unknowns which satisfy the equations. The book aims to give a method of finding the complete solution of a given system of linear equations, which is sufficiently systematic to be applied to any number of equations in any number of unknowns. While the actual process used is not much more than the familiar elimination of the unknowns, the point of view emphasizes the relation of the general problem to the simplest case.