Linear Algebra, 2/e, 2nd Edition

2

Systems of Linear Equations

2.1  INTRODUCTION

This chapter is a leisurely but exhaustive treatment of systems of linear equations and their solutions. The chapter begins by looking at the well-known procedure of row reduction of systems of linear equations for obtaining their solutions and thereby develops the important theoretical machinery of row and column operations. We also initiate the study of linear equations by using matrix operations in this chapter. The application of matrix methods yields useful insights into other entities such as invertible matrices. This chapter also introduces the important idea of determinants and develops its properties.

Note: from now onwards, we shall be writing a column vector as the transpose (x₁, x