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

Wrath of Math
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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
Row Echelon Form Explained: • Row Echelon Form of th...
Gauss-Jordan Elimination: • Guide to Gauss-Jordan ...
Gaussian Elimination Example Problems: (coming soon)
Linear Algebra course: • Linear Algebra
Linear Algebra exercises: • Linear Algebra Exercises
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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1 авг 2024

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Комментарии : 44   
@WrathofMath
@WrathofMath 23 дня назад
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! ru-vid.com/show-UCyEKvaxi8mt9FMc62MHcliwjoin Linear Algebra course: ru-vid.com/group/PLztBpqftvzxWT5z53AxSqkSaWDhAeToDG Linear Algebra exercises: ru-vid.com/group/PLztBpqftvzxVmiiFW7KtPwBpnHNkTVeJc
@julieye2260
@julieye2260 3 месяца назад
Excellent work. Thank you so much!
@ShermukhammadKarimov
@ShermukhammadKarimov 2 месяца назад
thanks for clear explanation
@inkbledsmurfett
@inkbledsmurfett 5 месяцев назад
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
@WrathofMath
@WrathofMath 5 месяцев назад
So glad it helped, thanks for watching!
@prachitisharma
@prachitisharma 9 месяцев назад
your way of explaining is awesome
@WrathofMath
@WrathofMath 9 месяцев назад
Thank you!
@enakpomugrace654
@enakpomugrace654 3 месяца назад
You just saved me, I have exam tomorrow and I now fully understand the topic❤
@WrathofMath
@WrathofMath 3 месяца назад
Glad to help, thanks for watching and good luck on the exam!
@hrudhaianand3886
@hrudhaianand3886 3 месяца назад
BRO SAMEEEEE THANKS A BUNCH!!!!
@PunmasterSTP
@PunmasterSTP 21 день назад
How'd your exam go?
@PunmasterSTP
@PunmasterSTP 21 день назад
@@hrudhaianand3886 How'd you do on your test?
@aadreejapandey3436
@aadreejapandey3436 Месяц назад
awesome video can solve now
@WrathofMath
@WrathofMath Месяц назад
Glad I could help!
@mahamoudmaash5145
@mahamoudmaash5145 10 месяцев назад
amazing video very well explained
@WrathofMath
@WrathofMath 10 месяцев назад
Thank you!
@PunmasterSTP
@PunmasterSTP 21 день назад
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" 😆
@t3chwali598
@t3chwali598 9 месяцев назад
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?
@SuperVazz
@SuperVazz 2 месяца назад
Thanks, great video. Very helpful. :)
@WrathofMath
@WrathofMath 2 месяца назад
Thank you!
@ZhihuiLu-ov2mw
@ZhihuiLu-ov2mw 2 месяца назад
thank you!!
@WrathofMath
@WrathofMath 2 месяца назад
You're welcome - thanks for watching!
@user-qo5sl2vc2l
@user-qo5sl2vc2l 6 месяцев назад
nice work.....
@WrathofMath
@WrathofMath 6 месяцев назад
Thanks!
@djdanzo206
@djdanzo206 5 месяцев назад
love from south africa
@manitpaulose
@manitpaulose 5 месяцев назад
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?
@aram5642
@aram5642 2 месяца назад
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?
@anastasiakatsantoni7689
@anastasiakatsantoni7689 2 месяца назад
most people will do it automatically and not even take a minute to question why, so good job for asking! From my understanding it's so you immediately get an answer for a variable. i.e., in a 3x3 matrix you instantly get z=6 if the other two variables are 0. And you move upwards to get all of the answers by substitution.
@PunmasterSTP
@PunmasterSTP 21 день назад
I think it's mostly just a convention, and if you're ever unsure about why or how matrices can be used to solve systems of equations, just remember that they are a shorthand. Basically you're just writing down the coefficients and not the variables to save a bit of writing.
@omarkhalily4369
@omarkhalily4369 9 месяцев назад
Are yall doing all this in alevels?
@shin-ishikiri-no
@shin-ishikiri-no 4 месяца назад
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?
@WrathofMath
@WrathofMath 4 месяца назад
Yes those are all subscripts for x, they are just distinct variables in the system.
@anon8867
@anon8867 Год назад
Aye yo firsttttttttttt!!!!! Hand me my 🏅 nowwwww !!!!!!
@WrathofMath
@WrathofMath Год назад
Here you go champ🏅 When the mob of people studying linear algebra discover this video, they will salute you!
@naphilim6666
@naphilim6666 Год назад
@@WrathofMath Is there a silver medal
@ashishtiwary7947
@ashishtiwary7947 11 месяцев назад
take my salute , just discovered this osm channel
@OsamaSalih-SAS
@OsamaSalih-SAS 11 месяцев назад
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
@sathyaskitchen7386
@sathyaskitchen7386 Месяц назад
What if the first number is 3 ??
@edlitam5774
@edlitam5774 11 месяцев назад
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.
@routernobe
@routernobe 9 месяцев назад
I know it's a bit late, but if I'm not mistaken that is gauss Jordan. This is gaussian
@ohhhhhspam2321
@ohhhhhspam2321 9 месяцев назад
That rule applies to row reduced echelon form. These matrices are in reduced echelon form.
@djdanzo206
@djdanzo206 5 месяцев назад
its funny how everyone who does linear algebra uses this textbook,nno matter where you are from
@eliassheikh738
@eliassheikh738 4 месяца назад
Which textbook is he using?
@PunmasterSTP
@PunmasterSTP 21 день назад
@@eliassheikh738 He says the name of the text at 1:05. It's Elementary Linear Algebra by Howard Anton.
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