7 - MATRICES AND DETERMINANTS

Abstract

This chapter discusses matrices and determinants. The material on matrices and determinants serves as an introduction to linear algebra, a mathematical subject that is used in the natural sciences, business and economics, and the social sciences. As matrix methods may require millions of numerical computations, computers have played an important role in expanding the use of matrix techniques to a wide variety of practical problems. A system can be displayed by a matrix, which is simply a rectangular array of mn real numbers arranged in m horizontal rows and n vertical columns. The numbers are called the entries or elements of the matrix and are enclosed within brackets. If the numbers of rows and columns of a matrix are both equal to n, the matrix is called a square matrix of order n. In the system of linear equations, the matrix in which the first column is formed from the coefficients of x and the second column is formed from the coefficients of y, is called the coefficient matrix. The matrix that includes a column consisting of the right-hand sides of the equations, separated from the other columns by a dashed line, is called the augmented matrix.