Gaussian Elimination & Row Echelon Form

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This precalculus video tutorial provides a basic introduction into the gaussian elimination - a process that involves elementary row operations with 3x3 matrices which allows you to solve a system of linear equations with 3 variables. You need to convert the system of equations into an augmented matrix and use matrix row operations to write it in row echelon form. Next, you can convert back into a system of linear equations and solve using back substitution.
Full-Length Math & Science Videos:
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Introduction to Matrices:
• Intro to Matrices
Adding and Subtracting Matrices:
• Adding and Subtracting...
Scalar Multiplication of Matrices:
• Scalar Multiplication ...
Solving Matrix Equations:
• Solving Matrix Equations
Multiplying Matrices:
• Multiplying Matrices
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Gaussian Elimination & Row Echelon Form:
• Gaussian Elimination &...
Gauss Jordan Elimination:
• Gauss Jordan Eliminati...
Gaussian Elimination With 4 Variables:
• Gaussian Elimination W...
Inverse of a 2x2 Matrix:
• Inverse of a 2x2 Matrix
Inverse of a 3x3 Matrix:
• Inverse of a 3x3 Matrix
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Determinant of 2x2 and 3x3 Matrix:
• Determinant of 3x3 Mat...
Determinant of 4x4 Matrix:
• How To Find The Determ...
Cramer's Rule - 2x2 Linear System:
• Cramer's Rule - 2x2 Li...
Cramer's Rule - 3x3 Linear System:
• Cramer's Rule - 3x3 Li...
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Final Exams and Video Playlists:
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Опубликовано:

20 июл 2024

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Комментарии : 807

@TheOrganicChemistryTutor Год назад

Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections Next Video: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-eYSASx8_nyg.html

@user-oz2ei2qo7r 4 месяца назад

Thank you 🙏

@jasonchen3507 3 года назад

This guy explains it so well...my textbook explains it like a brick.

@thedisneyravenclaw1401 3 года назад

For real though

@zinkeyminaze7018 3 года назад

true I wonder if he is a teenager he got suvh a sweet sound

@RicardoGonzalez-wq8tp 2 года назад

@@zinkeyminaze7018 He's got the voice of an angel sent from the math gods

@llynn4206 2 года назад

Textbook is pretty much a piece of brick

@abbasidafftah768 2 года назад

Really, where r uh from

@droomahbroo9291 2 года назад

This man carried me through 1st year and now hes carrying me through honours as well. You are a true legend!

@aimokoivunen4787 2 года назад

Best of luck!

@master_baiter1873 Год назад

His exapmles are ass though. He picks the easiest examples. He could give a harder one.

@droomahbroo9291 Год назад

@@master_baiter1873 well he’s not going to do ypur homework for you :D. I usually watch the video to learn the basic concepts and then go through the examples and exercises given in class. I then use his examples to boost my confidence the morning of the test. Seems stupid but its gotten me through Physics 5 so…

@master_baiter1873 Год назад

@@droomahbroo9291 i mean he could give one hard example. He chose easy examples. Ones i can easily do in my head.

@GoToMan Год назад

@@master_baiter1873 I suggest you pick up Strang's linear algebra

@mrguys2822 Год назад

Your videos are so much easier to understand than my lectures. Thank you for carrying me through university xD

@amreenaym786 Год назад

Y’all are learning this in uni? Bro I’m having a hard time understanding this and I’m a freshman in hs

@higgsboson6274 Год назад

@@amreenaym786 just keep going, keep practicing. things will make sense eventually

@suraboss2673 Год назад

@@amreenaym786 its literally going to be easy learning this in university

@josiahscarrmusic6750 Год назад

@@amreenaym786 you do repeat stuff to regain that familiarity, though I am learning this cause I have a maths module as part of my CS degree

@oluwakoredeonasanya3267 Год назад

@@amreenaym786 in my country we don't learn this stuff in high-school, so I'm learning this for the first time in university

@kastriotselimi7444 Год назад

I have an exam tomorrow,and I’ve been trying to learn this from scripts of my teacher for 3 hours and there is a guy like you that teach me all the stuff for 18 minutes.I wish you a good health and life.Thank you

@taekwondotime 6 лет назад

This seems to be a common misunderstanding with matrices. *Echelon form is simply the final matrix after you've finished Gauss elimination* . (The matrix at 6:10.) It need only have 0's in the lower left-hand corner. *There is no requirement to have 1's along the main diagonal because they do not help in solving the problem* . They are simply wasted operations and are not done in practice. (Unless you want to do Gauss-Jordan elimination... which is also not used in practice.) People seem to confuse the two. You only need 1's on the main diagonal if you're prepping for Gauss-Jordan elimination which then transforms the numbers in the upper right corner of the matrix to 0's as well. If you're not doing Gauss-Jordan, then don't worry about having 1's. *Once you obtain the matrix @**6:10**, then we know that 4z = 8 and therefore z = 8/4 = 2* . From there we use back substitution to solve for the remaining variables. FYI: This is straight out of my math textbook if you don't believe me. *Source: Advanced Engineering Mathematics by Erwin Kreyszig*

@taekwondotime 6 лет назад

TIP: The *scale* operation is your friend! As soon as you start getting into non-trivial matrices where the coefficients don't eliminate nicely, use the scale operation to get them up to a common value and then eliminate them. This helps you avoid ugly fractions and awful decimal numbers that have infinite precision. For example, consider the following system of equations: x + y - z = 9 8y + 6z = -6 -2x + 4y - 6z = 40 Without using the scale operation, you'll hit a wall by about step 3.

@pablonapan4698 5 лет назад

Thanks

@dami4271 5 лет назад

@@taekwondotime so whats the scale operation

@WTHnada 5 лет назад

You should have explained that in the video I was so confused :(

@alsudairy.k5647 5 лет назад

The one he did is called Reduced Row Echelon form.

@israel4101 5 лет назад

This RU-vid channel is literally my first year of my BSc's saving grace. I can't thank you enough.

@KingNat. 4 года назад

Not even first year bruh, you can use some of this stuff for second year too. This man got me through calc in first year CS

@youssefbayoumi2694 3 года назад

can i minus 2 rows ?? someone answer plz

@PenandPaperScience 3 года назад

@@youssefbayoumi2694 What exactly do you mean? You can indeed add a row with minus 2 times another row.

@icebearreal 2 года назад

@@PenandPaperScience Hi! I am one of your subs.

@icebearreal 2 года назад

@@PenandPaperScience I'm glad to find you here.

@mosessydneyruiz87 3 года назад

I am here because of the online class. Self-study huhu. Like also if this is your case! Goodluck to all of us!

@Rob-J-BJJ 3 года назад

haha yeah im taking linear algebra online

@annedeborah5926 3 года назад

Same reason 😅 All the best to you too!!!

@RealSupaHotFireVEVO 3 года назад

@@Rob-J-BJJ Same here lmao.

@americanconsumer4496 3 года назад

Same!!!!!! Tough stuff

@Anand-zt3wv 3 года назад

Where we at gang?!!!!!!!!!!

@tenyshaross-vanmierlo7163 6 лет назад

This youtube channel is literally my first year of my BSc's saving grace. I can't thank you enough.

@ddahstan6876 2 года назад

One of the most humble educators that we're blessed with! A heartfelt Respect to your dedication and patience because a lot of us will survive much longer in math, or even feeling more motivated!! 🍭

@AFCOE Год назад

What I wonder is that his title is chemistry tutor😂😂😂. But teaching math more than math teachers😅😅😅😅

@kipiekiee519 10 месяцев назад

I just wanna say, you've helped me so much over the past year. Precalc, calc 1, a calc 2 crash course over the summer, and now linear algebra. I doubt i'd of been able to understand everything as much as I do now without your videos helping us walk through each new method and idea. Thank you for taking the time you have to help us learn

@EmilyBrownn 3 года назад

I am in maths major and this year is my second year in this department. Before online education, I was learning with your videos. Actually my college is very hard but you solve easy question,so I love your videos, because I feel like I am a paradox in class of my teachers. It is very awful situation. I am so glad to discover this channel thanks the organic chemistry tutor

@ninjapirate123 2 месяца назад

have u graduated already?

@jackdeily8615 4 года назад

My brain does not let me do this. I have been trying so hard for a week and I feel like my head is going to explode.

@girlytomboyja7 4 года назад

Same here brother :(

@Phenomenal268 4 года назад

Currently stuck myself.

@aimanhakim4935 4 года назад

same

@mortisea2408 4 года назад

bro its like if the devil tried to make sudoku

@alicewang5398 4 года назад

same

@hybe8459 2 года назад

يبني والله ال انت بتعمله ده عظمه فشخ ربنا يخليك لينا كلنا بنحبك والله كل ال في هندسة حلوان المطرية بيحبوك والله و بيشكروك على مجهودك معانا انت راجل محترم و ربنا هيكرمك و هيخلي عيالك يبقوا احسن ناس في الدنيا حبيبي يا دوك

@martinvich5796 9 месяцев назад

couldnt agree more. xddd

@farismohamed7048 2 месяца назад

ههههههههههه

@georgesadler7830 2 года назад

MR. Organic Chemistry Tutor, this is an excellent introduction to the Gaussian Elimination Method and Row Echelon Form in classical Linear Algebra. Linear Algebra is very useful in different levels of mathematics.

@MARIN-py9ye 3 года назад

My prof. explained this to me 3 times and I didn't get it, watched your video one time and figured it out instantly. Perfect job on the tutorial, thank you!!!

@EPICGamer516 2 года назад

You currently are my savior for taking linear algebra! Thank you for doing such great work for the world!

@starfut6318 Год назад

Best teacher any comrade desires! 👏🏻👏🏻

@dania8183 4 года назад

A THANK YOU COMMENT IS NEVER ENOUGH TO YOU GUYS!!!! LIFE SAVERS!!! THANK YOU VERY MUCH TEACHER, THE ORGANIC CHEMISTRY TUTOR.

@paulvanbrakel 9 месяцев назад

For the people that get confused at 10:50: 'R3 = R1-R3 is the same as 'R3 = -R3 + R1. He writes it in a different way, but you're still working on 3R in both cases

@parthbhanushali9382 8 месяцев назад

thanks a ton mate

@muhammedowais8541 8 месяцев назад

Thanks man now i think i understand.

@sreekumarnair-rl2wo 6 месяцев назад

I don't understand it why it's R3=-R3+R1 we can directly go with R3=R3-R1 isn't it? Please help me with this

@oimatesimro2088 6 месяцев назад

@@sreekumarnair-rl2wo i think its because you have to write the ending row (R3) at the end of your operation, he explained it in another matrix vid, i think its the row operation vid

@ckaamuli8182 3 месяца назад

@@oimatesimro2088 wouldn't R3 = -R1+R3 work then?

@joanhewitt-fagan2815 5 лет назад

thanks. you are absolutely the best, my math teacher totally confused the class with this principle.

@kreedapanda7741 5 лет назад

I wish this guy was my math lecturer.

@BigBrother4Life 5 лет назад

They always do the easiest question on the internet.

@TheGunzSkido 5 лет назад

well you only need the basic anyways for this kind of question.

@dabigboom2426 5 лет назад

@@TheGunzSkido Naaw bro im in Algebra 2 and my questions are hard af

@TheGunzSkido 5 лет назад

@@dabigboom2426 keep learning bro. You can do it

@canerc6668 4 года назад

Otherwise we could be afraid of how difficult it may be : )

@ashleybellinghoven2331 4 года назад

Ahmed01 I know !!!

@lovelya72 Год назад

Thank you so much for the explanation! I can't understand this in my textbook and all and you only took 20 minutes for me to completely understand this concept!

@aimokoivunen4787 2 года назад

Felt so lost after my professor taught this. Came here for help as always. Was not disappointed. You're a good man. Thankyou

@azizalaliq8 5 лет назад

This RU-vid channel is literally my first year of my Beng's saving grace. I can't thank you enough.

@CptMaahir 3 года назад

Did you find his thermodynamics vids helpful?

@lesegoesther7876 Год назад

You man😫😫🔥🔥🔥🔥🔥The best of the best!We love you here in Limpopo!❤️

@thedrumminggamer1064 9 месяцев назад

your videos are 10x more informative than any lecture i have sat , keep up the good work

@timothylittlefield 2 года назад

You corrected both z=2 and -2 in the top row. Great job and thank you! I can solve variables using Gaussian elimination.

@dazzlingforests1373 2 года назад

Thank you for writing that he caught that! I was getting worried lol

@ez5267 3 года назад

We have an exam tomorrow, including this topic. Hoping to pass it.

@neilialopez7446 3 года назад

I have one tomorrow too cri.

@ahmetkarakartal9563 3 года назад

@@neilialopez7446 ahahaha me too

@tarylee357 3 года назад

updates? how was it! im having one soon :)

@PenandPaperScience 3 года назад

Hope it went well. And for those students out there that want some more practice on Gaussian Elimination, I've made a video where I solve such exercises step-by-step. It might help some :) ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-nyWp9sr8uGE.html

@StevesUniverse 3 года назад

UPDATE??

@dianaingato3067 5 лет назад

This just saved me.. I got my end of semester exam on Tuesday.. Hope this is going to help a big deal. Thank you.

@sukhoiboy4140 2 года назад

ive been a university student for 3 years now. Organic chemistry tutor is awesome! I remember the morning of a Calc two exam, other students asking how each other felt... I told them i reviewed some organic chemistry tutor videos their jaws dropped!!! hahaha. they didnt realise u did math lol. I love you man keep it up!

@timbarrett4580 9 дней назад

I literally didn't understand how this worked and my professor never really did any problems out. Watching you solve it made it seem so trivial. Thank you so much!! You are amazing

@hcxmedi3000 3 года назад

Your a legend. The way you teach. I learn everything from you.

@fafiethamae 3 месяца назад

All thanks to you sir ,now am doing my Electrical Power Engineering National diploma all because of you ... I passed my o levels thank to you ... God bless you❤❤❤❤❤❤

@jamesmunroe6558 7 месяцев назад

Simple, clear, and self-evident. Many thanks!

@undinesoul5261 3 года назад

dude, you're awesome, thanks so much, I was really struggling with this and this video has helped me so much. def gonna buy some merch

@emilytran212 5 лет назад

You've never failed me. I love you so much!

@user-sc4ds3dw4b 2 года назад

this guy is responsible for me to pass by engineering . thank you

@JhunsTV Год назад

This channel really is the best it could really relay the gist to it's viewers, those professor just make my life harder and complicated

@user-rv4zm8xm1d 4 года назад

You made this so much easier ! Thank you!

@NotEnoughAlpacas 2 года назад

He has been my saving grace in 5 different classes so far

@MoiraBrady Год назад

Thank you. You explained it so well and now I can practice this till I can do it without help. Really helpful and you have taken the stress out of my weekend :)

@lindamanas954 8 месяцев назад

Beautifully explained. Thank you. You are a fantastic teacher! I have watched a few of your matrices videos. I am a Maths teacher myself but I wanted to revise Gaussian elimination! Linda in the UK

@joshryanbligh5791 3 года назад

Thank you for the vid! Explained it far better than my instructor did!

@shereeannrichards3901 2 года назад

You made this so easy to understand and follow. For days I have been losing my sanity trying to complete my assignment on this topic. Thank you

@computersciencewithpeter 2 года назад

Love how you exemplified all the concepts...

@jinxinchan7981 4 года назад

Thanks. I am taking this class online this summer term. Reading the material for 19 times, I still doesn't understand. Now... there is hope :)

@ejuramusic 3 года назад

You are a saint! I just realized I forgot to do two math assignments and I needed to learn how to do this immediately

@lawrencemacharia3401 Год назад

Love how he explains everything in such a short time and detailed

@expansivegymnast1020 3 года назад

I will pass my Discrete Math class because of you. Thank you so much!

@williesolomon614 2 года назад

Impressive explanation. You're genius, I SALUTE you sir. Thank you and God bless.

@nightfox1416 Год назад

Great video! Only advice would be explain what you can do to simplify the matrix into row echelon form. For anyone watching, these are 1) You can swap the rows (you CANNOT swap the columns) 2) You can multiply the rows by any constant (in a similar way you would when solving simultaneous equations normally) except zero 3) you can add or subtract one row from the other (you see this often in this video)

@inarvii8181 Год назад

I am a bit confused as to why in the second example, he did R1-R3. Why would it not be R3-R1 so that it is 2-2?

@sonu1747 Год назад

@@inarvii8181 correct

@stephendemaine1426 2 года назад

Oh man, this just smacked me in the face, in a good way. Great breakdown. I am embarrassed to admit how much time I wasted with other resources before coming to this channel. I won't make that mistake again. Thanks for the insight!!

@sandismike3822 Год назад

The best tutor I've ever met....thank you sir

@user-oz2ei2qo7r 4 месяца назад

I had a hard time solving this but thanks to you it’s much easier 🎉

@rashidissa5887 3 месяца назад

Jack, me longer than a week, but have not lost hope. Never did matrix in my O-Level I am gradually catching up. Imagine in my late 70's, but still pursuing maths. I love it

@ryankeshet5820 4 года назад

Why are you so helpful all the time?

@normanhenderson7300 Год назад

I have not yet been acquainted with a video on this subject as yet that teach this method in a clear and systematic way. This one included.

@hiwotberhanu3814 4 года назад

He "in this vedio" Me"omg it's him 🤓🤓🤓"

@kopanokatebela8842 4 года назад

That is the feeling i always get, i even know before opening the video that it is him because of the colours he love using..

@cometolearn8598 2 года назад

Your a genius Keep going also you explain better than all my teachers :) 👏👏👏👏👏

@joanieLeventis3077 11 месяцев назад

I wish that I knew about this video while I was taking calculus in the university. It would have made things so much easier!!

@mathiasallon8368 Год назад

You really help me ...great teacher who I loves your tutorials

@jfrank622 Год назад

This guy and kahn, legends.

@mervynsookun5995 Год назад

You are a Pele or Maradona of a professor. Gifted genius !

@apheniesinegal2287 4 года назад

I love this RU-vid channel it helps and explains better than my professor

@OninabResources 4 года назад

Get more on Gaussian elimination method of solving systems of equations from this link ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-eXHOytiWWAw.html

@devOmarAZ 4 года назад

From Egypt>>>> Thanks ..... Your The Best : )

@caseysun8868 2 года назад

Thanks so much!! My final exam includes this content, I've forgot for a long time though. Hoping to pass!!

@josephkumwenda88 Год назад

Thanks man, this is helpful. You have saved my semester

@masterchi3ff Год назад

Thanks brotha for the assist, helped me through numerical exams 🙏❤️

@bigphuc 11 месяцев назад

Doing the lords work with this video, awesome explanation!

@Pinal375 Год назад

Thanks very much for such a good explaination. good work and hope to continue watching your new videos.

@mr.creepz Год назад

thanks bro you made me understand this topic in just 20 mins while my teacher was teaching it from 2 months

@PreferableFlavor 4 года назад

You are a god sent. Thank you for your easy to pick up informative videos

@OninabResources 4 года назад

Get more on Gaussian elimination method of solving systems of equations from this link ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-eXHOytiWWAw.html

@The_GreenHub Год назад

Bro it straight up WORKS. You gotta like a video that can explain A-Level maths to a 14 year old.

@iUmairBilal 4 года назад

Thank you so much sir ! your videos helped a lot many times. I am very thankful to you. keep doing good work.

@OninabResources 4 года назад

Get more on Gaussian elimination method of solving systems of equations from this link ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-eXHOytiWWAw.html

@shelematesfaye6672 5 лет назад

thanks for support to me online eduction my teacher of algebra

@Yusuf-sy6rb 7 месяцев назад

For the first example you could do this faster by eliminating 2 variables at once by adding first and second rows. For a 3 variable system of linear equations you can always eliminate any 2 numbers in the same column and then use those 2 rows with the zeros to eliminate another number in a different column (which is always doable because you can just use LCM for any of the other 2 columns). This is way faster than trying to directly get it in row echelon form from the start because you can solve for any variable first, not just the third column only for example.

@F4WKESofficial 2 года назад

When in doubt... the matrix is the way to go out! Most useful method IMO too

@diachyti Год назад

How did i understand it so easily i have been trying to read about this for hours no good, what 16 mins and now and am pumped up to do some math

@BigBlob7 9 месяцев назад

This was fantastic, completely lost in lectures but this is great!

@sophiaonyoutube Год назад

Awesome tutorial. Thank you so much!

@abdulasad8348 2 года назад

Passed my math exam coz of you. Thanks a ton :))

@kokopoppan 3 года назад

Nice vid soothing voice, maybe I will pass my test in 1 day :)

@texmexmunene5379 2 года назад

am grateful having your support. Please make videos concerning minors, cofactors and adjoint. in linear algebra.

@jasonsavard2819 Год назад

absolutely legendary ass guy. i cant believe im actually understanding everything clearly

@jessawatipachavula7852 Год назад

This video has really helped me, all thanks to you

@MsAlarman 2 года назад

Excellent explanation! A ton of patience !

@LS19981 2 года назад

Hours of reading about Gaussian elimination doesn't measure up to the first 2 minutes and 28 seconds of this video. Thank you.

@yayraatadja153 Год назад

this guyyyyyyyyyyyyyyyy......from saving me weeks to exams to helping me finish entire courses before midsem

@musebeonyango8958 2 года назад

You're my lecturer 100%💪💪good work

@topfootball8211 3 года назад

I come here after class and understand everything clearly.This guy is such a helper

@paulrbgt5562 3 года назад

same

@youssefbayoumi2694 3 года назад

can i minus 2 rows ?? someone answer plz

@nagwaezzat333 4 года назад

i like your way of explanation you are perfect

@justrandom3849 2 года назад

Thanks so much for this video Very simple and clear

@abugslife2461 3 года назад

let's gooooo linear algebra!! i passed calc 1 because of you!!!!

@Rajivrocks-Ltd. Год назад

For Row echelon form the leading coeffients of a row which are nonzero do not need to be 1, they can be any number as the theorem states. For the reduced row echelon form they do need to be 1 among other things.