Jun 07 2021 - Video Course (1 hr 22 mins)

This course will help you develop a deeper understanding of the theory of linear equations, linear systems, equivalent systems, echelon form, reduced row echelon forms, row reduction and gain the mathematical knowledge and skill level required to answer questions about linear systems. This course will teach you how to solve linear systems using elimination methods, Gaussian elimination, and Gauss Jordan reduction.

Created by Steve Warner

Linear Algebra

This course includes:

- 1 hr 22 mins of video courses
- Full lifetime access
- Go at your own pace
- Certificate of completion

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What you'll learn

Students will learn how to solve linear systems of equations and answer theoretical questions about linear systems

Requirements

Knowledge of basic algebra concepts is helpful.

1 Unit -
8 video lessons

What is a Linear Equation?

In this video, you will learn about linear equations in two variables, three variables, and four variables with examples. Sometimes, we use the word ‘unknowns’ instead of the word ‘variable’. I will also give you examples of nonlinear equations, and you will learn about a solution to linear equations with examples.

06:01

Linear Systems

A linear system is a collection of one or more linear equations involving the same variables. A solution to the linear system is a sequence that satisfies each equation in the system. In this video, you will learn about the linear systems with examples, solutions to the linear system with examples, and the solution set of a linear system.

08:39

The Elimination Method

The elimination method is useful for solving small linear systems. In particular, the elimination method works really well for solving systems of two equations with two variables. In this video, you will learn how to solve linear equations using elimination methods with examples.

09:17

10:53

Echelon Form

A matrix is in row echelon form if it satisfies three conditions. In this video, you will learn about the three conditions satisfied for a matrix to be in row echelon form with examples.

11:46

Row Reduction

Row reduction is a 4-step algorithm used to produce a matrix in row echelon form. This algorithm is also known as Gaussian elimination. A 5th step can be added to produce a matrix in reduced row echelon form. In this case, the algorithm is called Gauss-Jordan Reduction. In this video, I will use an example to walk you through the algorithm of row reduction. I will show you how to do both Gaussian elimination and Gauss-Jordan reduction.

12:04

More Examples of Row Reduction

In this video, I am going to go through 2 more examples of the row reduction algorithm by following the rules step-by-step.

10:58