A Guide to Gaussian Elimination Method (and Solving Systems of Equations) | Linear Algebra

We go over a step by step algorithm for performing the Gaussian elimination method on a matrix. How to perform Gaussian elimination is simply to use a sequence of elementary row operations to transform a matrix into its row echelon form. We see several examples of Gaussian elimination and show how to use the resulting row echelon matrix to solve the system of linear equations it represents. This requires solving for leading variables then performing back substitution. #linearalgebra Join Wrath of Math to get exclusive videos, lecture notes, and more: https://www.youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join Row Echelon Form Explained: https://youtu.be/oXMPQ-6YnGA Gauss-Jordan Elimination: https://youtu.be/CK65GbUTk4g Linear Algebra course: https://www.youtube.com/playlist?list=PLztBpqftvzxWT5z53AxSqkSaWDhAeToDG Linear Algebra exercises: https://www.youtube.com/playlist?list=PLztBpqftvzxVmiiFW7KtPwBpnHNkTVeJc 0:00 Intro 9:16 Example 2 11:04 Example 2 Solving the System (No Parameters) 12:49 Examples 3 Solving the System (Parametric Solution) Get the textbook for this course! https://amzn.to/43xAWEz ★DONATE★ ◆ Support Wrath of Math on Patreon: https://www.patreon.com/join/wrathofmathlessons ◆ Donate on PayPal: https://www.paypal.me/wrathofmath Follow Wrath of Math on... ● Instagram: https://www.instagram.com/wrathofmathedu ● TikTok: https://www.tiktok.com/@wrathofmathedu ● X: https://x.com/wrathofmathedu ● Facebook: https://www.facebook.com/WrathofMath