Systems of Linear Equations

Systems of linear equations in n variables: 

Linear equations in two variables: 

General Form: ax+by=0

Example: x+2y = 0 

Linear equations in 3 Variables: 

General Form: ax+by+cz=0

Example: 2x+6y+z=0

A linear equation in n variables x1,x2,X3, ... ,Xn has the form 

a1x1+a2x2+a3x3+. . . +anxn=b . 

The coefficients a1,a2,a3, ... , an are real numbers, and the constant term b is a real number. The number a1 is the coefficient's leading, and x1 is the variable's leading. 

* Linear equations have no products or roots of variables involved in trigonometric, exponential, or logarithmic functions. Variables appear only to the first power. 

Examples of linear equations: 

1) 3x +2 y-z = 0 

2) x +2 y = 4 

3) 7x-3y +2 z = 4 

*In general, there are only 2 types of Systems in Linear Equations. Consistent and Inconsistent Systems. 

What is Linear Algebra?

This is the branch of Algebra in which one studies vector (linear) spaces, linear operators (linear mappings), and linear, bilinear, and quadratic functions (functionals and forms) on vector spaces.

(Encyclopedia of Mathematics, Kluwer  Academic Press, 1990)

The study of Linear Algebra demands familiarity with Algebra, Analytic Geometry and Trigonometry.

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