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

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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)

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[WrathofMath]

Help me finish this course by joining Wrath of Math to access exclusive and early linear algebra videos, plus lecture notes at the premium tier!

[enakpomugrace]

You just saved me, I have exam tomorrow and I now fully understand the topic❤

[inkbledsmurfett]

I been trying to plug n chug with a sprinkle of brute force into REF this gave me a clear path in less than 5 minutes. You are a godsend

[PunmasterSTP]

Gaussian Elimination? More like "Great videos and information!" 👍

Also, did you hear about the chiropractor that switched clients out using Gaussian Elimination? There was a lot of "back substitution" 😆

[SuperVazz]

Thanks, great video. Very helpful. :)

[tchwali]

Really neat way of explanation here. Thanks ! A question about the free variables: does this mean that I can plug in any value for x2 and x4 for the first example and I can solve the original matrix?

[aram]

I've never had it in school and learning on my own, so please excuse my ignorance. Why is it essential to have all-zeros rows at the bottom of the matrix?

[shin-ishikiri-no]

When you say x2, x3, x4, x5, ...etc. the numbers themselves are just for organizational purposes, correct? It seems like you are just using the notation to keep track of the various manipulations. Are these technically subscripts of x?

[manitpaulose]

Hi @Wrath of Math
At 05:06, the 3rd row got transformed from [ 0 0 5 0 -17 -29 ] to [ 0 0 0 0 1/2 1].
if we did R3 + R1 to make the -5 to 0, then it would ne [ 0 0 0 3 -13 -15 ]
Am I missing something?

[edlitam]

Excellent video but I have one question: shouldn’t the columns containing a leading 1 have 0s everywhere else? In the first example in columns n3 and n5 there are leading zeros but in those columns there are also other numbers different from zero.

[OsamaSalih-SAS]

In 4 ×4 matrix with this method sometimes you get the right arrangement of row zero but the values of 4 variables will be different who know the right arrangement of the rows operation plz

[djdanzo]

its funny how everyone who does linear algebra uses this textbook, nno matter where you are from