Advanced Engineering Mathematics, 7th Edition

8.2 Systems of Linear Equations

INTRODUCTION

Recall, any equation of the form ax + by = c, where a, b, and c are real numbers, is said to be a linear equation in the variables x and y. The graph of a linear equation in two variables is a straight line. For real numbers a, b, c, and d, ax + by + cz = d is a linear equation in the variables x, y, and z and is the equation of a plane in 3-space. In general, an equation of the form

a₁x₁ + a₂x₂ + . . . + a_nx_n = b_n,

where a₁, a₂, . . ., a_n, and b_n are real numbers, is a linear equation in the n variables x₁, x₂, . . ., x_n .

In this section we will study systems of linear equations. Systems of linear equations are also called linear systems.

General Form

A system of m linear equations in n variables, ...