Systems of Linear Equations Introduction

In this video I give the definitions of a linear equation, a system of linear equations, a solution of a system of linear equations, and the solution set for systems of linear equations. I work through examples (5:39) finding the solution set of given systems of linear equations in 2 variables by graphing the equations in the system. I show geometrically that any system of equations in two variables must have either 0,1, or infinitely many solutions. Next we extend this idea and state the theorem that says that every system of linear equations has either 0,1, or infinitely many solutions (9:51); then I prove the theorem. Lastly, I introduce the notion of a consistent and inconsistent (14:07) linear system and provide some examples of consistent/inconsistent linear systems.

Video Outline:
Definition of Linear Equation (:08)
Examples of Linear Equations (0:43)
Definition of Systems of Linear Equations (1:23)
Examples of Systems of Linear Equations (1:31)
Definition of Solution of System of Linear Equations (2:32)
Example - Finding Solution of a System (3:39)
Definition of Solution Set (5:27)
Examples - Finding Solution Set of Given Systems (5:39)
Theorem (9:51)
Theorem states that a system of linear equations has
1. no solution, or
2. exactly one solution, or
3. infinitely many solutions
Proof of Theorem (10:03)
Definition of Consistent/Inconsistent Linear System (14:07)