Chapter 2 - DETERMINANTS

Abstract

This chapter focuses on determinants. Every square matrix has associated with it a scalar called its determinant. Given a square matrix A, a minor is the determinant of any matrix formed from A by the removal of an equal number of rows and columns. To find the determinant of a matrix A of arbitrary order, (1) pick any one row or any one column of the matrix—dealer's choice, (2) for each element in the row or column chosen, find its cofactor, and (3) multiply each element in the row or column chosen by its cofactor and sum the results. This sum is the determinant of the matrix. The chapter discusses some useful properties of determinants. Most of these properties are presented in terms of row operations; they are, however, equally valid for the analogous column operations. If one row of a matrix consists entirely of zeros, then the determinant is zero.