Systems of Linear Equations (and System Equivalency) [Video]


Dave4Math » Linear Algebra » Systems of Linear Equations (and System Equivalency) [Video]

I begin with 2 by 2 and 3 by 3 linear systems of equations. I then discuss consistent and inconsistent systems of linear equations and work through several examples. The general system of linear equations is defined, and parametrizing a solution set of a linear system is demonstrated. I explain augmented matrices, row operations, and when two linear systems of equations are called equivalent.

Have you ever wondered how to solve problems with three or more variables? Have you ever worked with several equations where each equation has several variables? In this video, I am going to show you how to work with systems of linear equations.

Hi, I’m Dave, welcome back to my channel.

In today’s episode, I’m going to show you the in’s and out’s of systems of linear equations. Then I’ll discuss consistent and inconsistent systems. After that, I explain what equivalent systems are and row operations. This video is for anyone getting ready to study Gaussian elimination, such as a Linear Algebra student just starting.

Let’s get started.


How do you solve systems of linear equations?

Solving is often done by eliminating variables one by one until the systems are small enough, then using backtracking to find the complete solution set.

What are the three methods for solving systems of equations?

Systems of Linear Equations General matrix form isolated on white background The matrix is of dimension m x n

There are three standard methods for two by two systems of linear equations: elimination, substitution, and graphing. While elimination and substitution are just variances of the same process, the graphing approach becomes impractical for larger systems.

What are the three types of systems of linear equations?

The solution set can classify a linear system of equations. Either there is a unique solution, no solutions, or infinitely many solutions. These are the only three possibilities.

When are two linear systems called equivalent?

Two systems of linear equations are equivalent when they have the same solution set. In other words, when the linear systems represent the same geometric object, the linear systems are equivalent.


Now I wanna turn it over to you. 

What’s the largest linear system that you ever have solved by hand? Either way let us know what you think in the comments below right now.

If you like this article or the video, please like or leave a comment and subscribe to my channel.

dave at dave4math

David Smith (Dave) has a B.S. and M.S. in Mathematics and has enjoyed teaching precalculus, calculus, linear algebra, and number theory at both the junior college and university levels for over 20 years. David is the founder and CEO of Dave4Math.