This is the first part of a full linear algebra course. This part of the course focuses on the theory of linear systems.
In this part of the courseyou will
learn how to solve linear systems.
develop a deeper understanding of the theory of linear systems.
gain the mathematical knowledge and skill level required to answerquestions about linear systems.
Course Lessons
What is a Linear Equation
Linear Systems
Elimination Method
Equivalent Systems
Echelon Form
Reduced RowEchelon Form
Row Reduction
Row Reduction - More Examples
In the first lesson, you will learn the definition of a linear equation and what it means to be a solution of a linear equation.
In the second lesson, you will learn about linear systems, solutions of linear systems, and the solution set of a linear system. You will also learn about the three types of solution sets of linear systems. Every linear system has either a unique solution, no solution, or infinitely many solutions.
In the third lesson, you will learn how to use the elimination method to solve small linear systems with two equations and two variables.
In the fourth lesson, you will learn what it means for two systems to be row equivalent and the operations you can perform on systems to generate equivalent systems.
In the fifth lesson, you will learn to recognize when a linear system is in echelon form. This is a form where the system can be solved pretty easily using a method called backsolving.
In the sixth lesson, you will learn to recognize when a linear system is in reduced row echelon form. This is an even nicer form then echelon form because the solutions to the linear system can be found very easily from this form.
In the seventh lesson, you will learn the methods of Gaussian Elimination and Guass-Jordan reduction to change a linear system to echelon form and reduced row echelon form, respectively.
In the eighth lesson, you will see enough examples so that you will be able to solve any linear system that you are given.
