## ELEMENTARY LINEAR ALGEBRA

**ELEMENTARY LINEAR ALGEBRA**

*K. R. Matthews

**1. Introduction to linear equations**

A linear equation in n unknowns x1. x2,…, xn is an equation of the form

a1x1 + a2x2 + … + anxn = b,

where a1, a2, …, an, b are given real numbers.

For example, with x and y instead of x1 and x2, the linear equation 2x + 3y = 6 describes the line passing through the points (3; 0) and (0; 2).

Similarly, with x; y and z instead of x1; x2 and x3, the linear equation 2x + 3y + 4z = 12 describes the plane passing through the points (6; 0; 0); (0; 4; 0); (0; 0; 3).

A system of m linear equations in n unknowns x1; x2; …; xn is a family of linear equations

a11x1 + a12x2 + … + a1nxn = b1

a21x1 + a22x2 + … + a2nxn = b2

…

am1x1 + am2x2 + … + amnxn = bm.

We wish to determine if such a system has a solution, that is to find out if there exist numbers x1; x2; … ; xn which satisfy each of the equations simultaneously. We say that the system is consistent if it has a solution. Otherwise the system is called inconsistent.

Advertisements
var o = document.getElementById('crt-2124938015');
if ("undefined"!=typeof Criteo) {
var p = o.parentNode;
p.style.setProperty('display', 'inline-block', 'important');
o.style.setProperty('display', 'block', 'important');
Criteo.DisplayAcceptableAdIfAdblocked({zoneid:388248,containerid:"crt-2124938015",collapseContainerIfNotAdblocked:true,"callifnotadblocked": function () {var o = document.getElementById('crt-2124938015'); o.style.setProperty('display','none','important');o.style.setProperty('visbility','hidden','important'); }
});
} else {
o.style.setProperty('display', 'none', 'important');
o.style.setProperty('visibility', 'hidden', 'important');
}
(function(g){if("undefined"!=typeof g.__ATA){g.__ATA.initAd({sectionId:26942, width:300, height:250});}})(window);

Categories: Free Book

Comments (0)
Trackbacks (0)
Leave a comment
Trackback