# Chapter 1Systems of Linear Equations and Matrices

## INTRODUCTION

Information in science, business, and mathematics is often organized into rows and columns to form rectangular arrays called “matrices” (plural of “matrix”). Matrices often appear as tables of numerical data that arise from physical observations, but they occur in various mathematical contexts as well. For example, we will see in this chapter that all of the information required to solve a system of equations such as

$\begin{array}{rrr}\hfill 5x+y& \hfill =& \hfill 3\\ \hfill 2x-y& \hfill =& \hfill 4\end{array}$

is embodied in the matrix

$\left[\begin{array}{rrr}\hfill 5& \hfill 1& \hfill 3\\ \hfill 2& \hfill -1& \hfill 4\end{array}\right]$

and that the solution of the system can be obtained by performing appropriate operations on this matrix. This is particularly important in developing computer programs for solving systems of equations because computers are well suited for manipulating arrays of numerical information. However, matrices are not simply a notational ...

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