Gauss Jordan Elimination & Reduced Row Echelon Form

This precalculus video tutorial provides a basic introduction into the gauss jordan elimination which is a process used to solve a system of linear equations by converting the system into an augmented matrix and using elementary row operations to convert the 3x3 matrix into its reduced row echelon form. You can easily determine the answers once you convert it to that form.
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
__________________________________
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
__________________________________
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...
___________________________________
Final Exams and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
/ collections

[@TheOrganicChemistryTutor]

Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections Next Video: kzbin.info/www/bejne/aoekialsrreIgrc

[@krave1324]

Thanks for the help my g

[@MusantoSus]

This guy is a literal blessing; the only sad thing is that people come to him only when it's too late - the night before the final.

[@suheyl-hx6sh]

well...the test is after 2 hours..

[@samuelomane-boadi5829]

It’s 2 hours before the paper 😢

[@jimihamtarou2913]

Me rn

[@lordoflobsters7254]

@@suheyl-hx6sh lmao same

[@jayPeezy1k]

literally me rn 2 hours before my exam rmfaooo

[@0m4r21o]

It took me 5 days to fully understand Gauss-Jordan Elimination. I have now, after many attempts, come to a conclusion that you ALWAYS have to do this when you start (the example is a 3x4 but the rule is for all): - - | 1 x x | x | | x x x | x | | x x x | x | - - - - | 1 x x | x | | 0 x x | x | | x x x | x | - - - - | 1 x x | x | | 0 x x | x | | 0 x x | x | - - After you have done these three steps you need to check if there’s a “1” in the middle of row two or three. If there’s no “1” in the middle of row two but there’s a “1” in row three, you need to swap row two with row three. If there’s no “1” in either, you have to find the pivot in row two and turn it into a “1”. These steps are the fundamental of Gauss-Jordan Elimination. The other steps will become clear after these steps.

[@maaz2004]

Bro you saved me thank you so much

[@deespace3744]

Nice 😮

[@spencerlevy345]

Legend comment. Never know what direction to take the questions in.

[@jd2981]

What do you mean by pivot?

[@bioshock5620]

@@jd2981I think the number in the row/column that u want to change

[@alexandravitale1360]

Matrices had me in literal tears while studying for finals. This helped so, so much, I can't thank you enough. Not one tutor I've been to has bothered to explain how we choose what row to work with or what numbers we choose. You've simplified it so much, thank you!

[@maindepth8830]

i am still confused as to how make this unholy disgusting garbage of a method to work

[@anycolouryoulike8567]

@@maindepth8830 Yup.

[@mm-ol6ed]

I’m literally in tears now typing this :(

[@swegmastur614]

@@mm-ol6ed appropriate profile picture

[@exactpeak5995]

@@maindepth8830 I might be a bit late but posting this here so other people don't have to go through the pain I did. So it turns out the order in which you choose what row to work with is irrelevant, as long as you calculate everything correctly. Some orders are more convenient than others but in the end all give the same answer. You might have to work a lot with fractions if you don't follow the convenient "path" but in the end it'll all check out.

[@Quashieyute]

bruh got me through Calc 2, now he's helping me in Linear Algebra, hopefully man dem have vids for Calc 3.

[@meanmole3212]

yup

[@dustybuiscits7424]

his calc 3 vids helped me so much

[@urextraaverageweirdo6124]

Guy has like every stem subject covered for you

[@Frankcohle]

You got linear algebra after calc 2? No wonder i’m finding this so hard, i haven’t even done calc 1 yet

[@highviewbarbell]

@@Frankcohle you don't really need calculus for linear algebra. many schools require calc 2 as a pre-requisite but I think it's totally unnecessary, you could do this right after a solid College Algebra class

[@hotrod4d]

My professors always explain things so fast I get hopelessly lost. You take your time to explain all the operations and I appreciate that

[@PavanKalyan-bo6qp]

bro get your brain checked

[@harristytydawg]

I should stop going to class and watch these videos.

[@DiasSaid99]

Tyrell Harris I said the same thing yesterday!

[@StigmaticGerm]

i started doing that 2 years ago and I've maintained solid grades doing so, he's very good at explaining all math concepts.

[@joodabed7816]

Me too👌

[@bbinbbinb]

No! Go to classes and watch videos. Do both, be more successful.

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Yeah Uni is kinda a scam

[@lekemorfaw4375]

@The Organic Chemistry Tutor has been very instrumental in my efforts to pass Mathematical Analysis & Linear Algebra here at college. This tutorial lessons are much more effective than what I get from school. Thanks a lot Sir for your work is wonderful. I´ll refer many others to this Channel.

[@PavanKalyan-bo6qp]

bro this is not music class to put instruments in you. go and study.

[@charless__10]

@@PavanKalyan-bo6qp You clearly don't understand simple english, i'm sorry for you

[@PavanKalyan-bo6qp]

@@charless__10 who asked?

[@violetboulevard3899]

@@PavanKalyan-bo6qp I asked

[@Random_sapiens]

​@@PavanKalyan-bo6qpThat's the point no one cares about your opinion and no one asked 😊

[@deeallo3690]

It seems so easy until you try solving one question 😭😭😭

[@kishtv4647]

😂😂😂😂😂😂

[@LasTvke]

Soo true😂😂😂

[@42luke93]

@@abdomenebadellah Does the order of finding the zeros matter? Do all zeros in this order before 1 right

[@loo524]

42luke yea It matters like u go fro row 1 to row 2 then row 3 for the bottom left. Then for the top right u go opp

[@nimikaattania9409]

For auto solution of gauss jorden method you can watch this tutorial to. Thnx me later kzbin.info/www/bejne/rKvRaWiaf7qZaa8

[@tamiawilliams4761]

My professor makes this seem so complicated but when you didn’t it was so easy.

[@abdouliebah6792]

he is ma sumperstar

[@meanmole3212]

Next time try learning a new thing with his teaching first and then listen your professor's explanation. You might find that suddenly your professor is a great teacher.

[@avrilynravenee5143]

@@meanmole3212 idk man, if you cant introduce a topic to your students in a way that they understand then youre still a bad teacher

[@cricticalthinking4098]

@@avrilynravenee5143 yeah likely you'll just feel like a smarty-pants as all the other students struggle with learning it for the first time. then you wonder why you showed up to lecture in the first place

[@VigneshVicky-zo5bk]

simp

[@christianlira1259]

Words larger than 'Thank you' for being the first person - ever - to show all the steps, and most importantly right at the very end, in what it means for x,y,z values. My Math understanding of rmatrices is so much clearer thanks to you. Totally appreciate you.

[@itisfridayanditwontbelong3020]

I'm a university student, and your videos help greatly to my lessons Thank you🌼

[@PavanKalyan-bo6qp]

Then quit University!

[@youtubenews178]

@@PavanKalyan-bo6qp that’s a dumb idea. You take college to get a degree and the certification that says you know how. Not to learn it unless you really want to

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You're a hero I hope you know that! Can't say enough how much I appreciate your videos! Especially as a bio student that struggles constantly with math.

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I cannot imagine how much u struggle with ur life wen u cant even do math

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[@PavanKalyan-bo6qp]

Go watch marvel.

[@ALGH2101]

Solving by both ADDing and SUBTRACTing rows instead of just always ADDing them may make some people prone to more errors when solving... You may have said it in the video, since I skimmed through, but for anyone who doesn't see it, when you ADD rows like ( R1 + R2 ) ONLY row R2 will CHANGE. And when you SUBTRACT rows like ( R1 - R2 ) ONLY R1 will CHANGE. My professor explained it to us as if there's no such thing as subtraction.. Since you can say... R1 + (-R2) = R1 - R2 I Always ADD rows and Never subtract so I can try and make it easier on myself to remember that only the right side of the addition problem will be the row that will be changed. For me, this is easier when I'm in a rush not to make mistakes. Because doing it your way just adds another step to think about and is something you need to consciously be aware of so you don't switch the wrong row. As an example at 5:40min in the video instead of your way.... 3(R1) - R2 {Where only Row 1 changes} I would do... -3(R1)+R2 {Where only Row 2 changes} I always ADD the rows and never subtract and just know the right side of the addition problem is the row that will be changed. This is just something that helped me make fewer mistakes and possibly save a few seconds time. Its good to get as many perspectives as you can though to find out which way is better for each individual.

[@theadel8591]

Hunter Keating This is exactly what I thought, I really figured from the beginning that there was something off because what I learned at college contradicts with his way which is directly subtracting one row from another but the correct operation says: you can add a multiple of one row to another row.

[@SM-qn7sr]

I do this too!!! It’s so much easier for me

[@HetrryParx]

Thanks a lot 🙏🏻

[@fadybassem9804]

you can simply assign the value of the operation to a row for example R1-R2 ---> R1 and this would be less likely to cause you errors while still substracting

[@ZavN11]

Literally just commented this, thanks alot!!

[@abassmobolaji9809]

It’s the way the lecturers here in my school make this easy concept so complicated. Thanks man , you deserve my respect.

[@rayenaouadi3190]

My teacher just linked this video for reference, a true G

[@flashbaq23]

Good luck!

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This guy got me through highschool. Absolute legend

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I really do not know who this guy is who is explaining BUT HE is a real Genius, his explanation is the BEST, very clear & to the point & I understand everything, THANK YOU SO MUCH

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Preparing for my math placement exam would be horrible with you!! Thank you for all you do. It's incredibly admirable. -Arin

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Without* you XD

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you sir carried me in organic chemisty 1 and 2 when i was doing my bachelor degree back then .. now im doing my master degree and u sir are doing the same thing but with math .. thank you so much!!

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Thank you so much!! In 10 minutes you manage to explain something that my professor is trying to explain to us in 3 hours

[@aerojohnson1208]

Outstanding Explanations. By far this channel is the Rolls Royce of Mathematics - The tutor is the Undefeated Champion proving a Supreme Clarity while he is standing out by Depth & Elegance 🙏

[@PavanKalyan-bo6qp]

Who asked?

[@ashketchum1244]

@@PavanKalyan-bo6qp i did

[@alinahussain4842]

I wish I came across this video before I had a mental breakdown trying to solve it myself

[@Exousia_TV]

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[@cemtolgamunyas4530]

same

[@InverseCr0wn]

me coming here before i even attempt it again and end up crying

[@Ntchindi_N]

You explain it wayyyy better than my lecture, God Bless👏🏾👏🏾

[@Artefic]

dudeeee i have a test tomorrow and i got stuck in this method 😭 your simple explanation with a simple example helped me grasp the concept very easily and i was actually able to solve a question from my school which i was stuck on, with ease!!! tysmm man you're such a saviour 😭🙏

[@GoodCat01210]

Im not following whats going on at 1:53. Your notation in the top right says you are going to be taking away R2 from R1 ( R1-R2 ) surely that should be the other way around ( R2 - R1 ). This also makes it so that its -1 - 1 = -2 which would have further implications on the rest of the calculation.

[@jonnygiger9794]

He is taking (R1-R2) and saving the result into the second row

[@ryanboi_69]

i seriously cannot use words to express how thankful i am to you.Thank you so much thank you.

[@muhammadrabbihossainsalafi9179]

I am a student of National University of Bangladesh .Really you convince quality is totally awesome.....tnx a lot my teacher .

[@MFuhaid-x8s]

Teacher at 5:53 u did a mistake because u wrote (3R1--R2) so we must change R2 not R1

[@idaliihernandesss924]

Omg Thankyou so much for this I want to cry because I finally got it 😭🥺❤️🙏🏼

[@agi6821]

thank you man. I always watch your thermodynamics video while i'm taking chemical engineering major. Now that i quit and change my major to statistic, i still watch your videos to help me study🤣

[@nelysvabska]

Very well explained! Thank you very much. All the professors should watch and learn how to explain the material properly. Thank you very much.

[@TheKt313]

6:00 isn't "R3" supposed to stay the same? It seems like you changed the "-6" to "6"

[@pow_ext]

Yeah i think that it is a mistake

[@pow_ext]

few minutes laters he corrected it :)

[@1213chio]

@@pow_ext what about the bottom left matrix at 10:50. Shouldn't that be -6 also?

[@waceabi]

@@1213chio he also corrected it later on in the video :-)

[@Mel-hv8zn]

When you pay for a professor to teach you these kinds of problems but ends up having to watch youtube videos to pass the class. I hate college

[@asadfarraj]

How you holding up now?

[@ShaikaAyeshaCariga]

how would you know that a certain operation is what you are going to use in every rows?

[@luciferx69]

It's just basic Arthimetic maths, to make numbers zero

[@megh.1278]

fucking around and finding

[@acecodm2550]

How did you know that at 2:36 we would have to use -2? Can someone explain this to me?

[@ember9947]

Thats the point withgaus-jordan questions.You DONT know what to do.You have to think of it yourself whatever solves the question.Its like solving a rubicks cube.You have to move the parts in a way which works for you and solve the cube.

[@King-gv4lg]

I think its better to convert the middle diagonal row to 1s first so its easier to acquire a value of 0 for the upper triangle portion of the matrix.

[@suhailraja7797]

No because when you try to get your zeros you mess up the main diagonal 1's the nice thing about having zeros first is that it's hard to accidentally get rid of because anything multipled by zero stays zeros

[@AP_483]

My exam starts in 2 hours. Thank you for this useful tutorial. This is so easy even kids can learn. Idk why some people hate this because they think that he's trying to confuse them. But nope, his explanation was crystal clear.

[@diogenesthecynic1334]

In the first part , you've calculated R1-R2 ( 01:50 ) and R1 has stayed untouched only R2 has changed , but later you've done 3R1 -R2 and the R1 has changed not R2. So when you're transforming the elements under the first diagonal , R1-R2 means that R2 is changing , and when you're above the diagonal , R1 is changing?

[@Termite1157]

@Divyansh Maurya thank you for responding I was confused on that part as well

[@learahme2991]

@@Termite1157what dis he say? I cant see his comment

[@franco6380]

Videos from yt carried me from high school to college thank u ur one of them.

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First you help me in cal 3 and now linear algebra thank u so much . Your videos surely deserve like from me

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This channel helps me in my campus Mathematics courses. At this rate ,I only go to class only to go back home and learn on this channel

[@riszkyhermawan2980]

i dont even go to campus man, i just enter a zoom room

[@darlene506]

God Bless you man! Thank you so much. this was so helpful... all the way from Sunny South Africa

[@TheGingaNinja11]

you’re the goat of youtube my man

[@rengiekago1850]

my new online teacher. My percale teacher does zoom or anything. She just hashes out notes and tests.

[@gemulostar1367]

To continue being quiet and not comment on your channel will be equal to committing a sin. You've been a great help to my little girl in Maths and since I can't pay you,I've decided to watch at least one advert anytime I open a tutorial of yours,not for my interest in their products but to support the channel😀 I just hope you get yours from the advertisers.😍

[@candacemarie4190]

I’m confused with the order of operations, I thought it went from a1,1 being the first step diagonally down and then a2,2 being the 4th step. Ile keep watching but I’m hoping Ile understand this.

[@Heroni66a]

Him: "So we are on route to get the correct answer" Also him 0 seconds later: "Actually I made a mistake" lol I love ur teaching btw very clear explanation!

[@cameliavirgo-evans5166]

istg this guy saved my life. RREF was a pain and linear algebra is basically RREF

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Көп рақмет! From Kazakhstan! much love!

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the ending... O M G! (read with Joseph Joestar's voice) Thanks. I own you a cup of coffee.

[@TheJaguar1983]

I was always taught to leave everything in the equation format and do the operations that way. For example: (x+y-z=7)-(x-y+2z=3)=(2y-3z=4) Basically the same thing, but without the matrix notation. I guess it comes down to how you learned it and what you're comfortable with as the result it's the same and the process is equivalent.

[@823studios]

This man has saved so many professors' jobs.

[@iancarlos9185]

Everything in mathematics is possible with the this guy. Thank You sir

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This monk really helped me for my bachelor's degree

[@hakinadedeji]

I've always said, and I will maintain, that the only relevant setting of knowledge after 2005 is the laboratory (2005 is the creation of KZbin and Vimeo and the start of a full online and social media age). Most classrooms are not worth it anymore because most teachers are not teachers, they are simply professionals with no passion at all to impart their knowledge. The Organic Chemistry Tutor is a teacher...he knows the stuff and can impart it clearly. We need more of him in schools all around the world, even in developed countries (I've been to 6 of them and very many of their teachers suck even though they have all the facilities and equipment). Keep up your good work and the earlier UNESCO realizes this the better.

[@rosette_renah]

You are a life savior because i was given some assignment on this ,of which i had no clue about this method.So i just came to your channel and BOOM i found it. Thank you.

[@natalieodonnell7136]

I dont even use my book anymore 😂 I go to the questions and find his video for it. Saves sooooo much time and writing. 🎉❤

[@GurkiratSingh-rd1yt]

Thank you man! I watched your video the day before the exam and it saved my life. During the exam was the first time I was row reducing by hand and I got it! Manh thanks!

[@goggler77]

Thank you, without you I couldn't pass the "Sesiune" :) You're the real MVP!!!!

[@diogenesthecynic1334]

La ce facultate esti?

[@georgesadler7830]

MR. Organic Chemistry Tutor, thank you for a fantastic introduction to the Gauss-Jordan Elimination Method and Reduced Row Echelon Form in Precalculus/Linear Algebra.

[@nonyabusiness665]

So where do I get what numbers to use or what tells me how to pick the rows? Big step to not mention

[@abdouliebah6792]

i must admit you having being saving me for a long time but this is just exceptional ma prof made it so complex i check most videos in youtude is da same you are ma super hero

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I remember when this dude was at 1M subs just at the start of COVID now look at him. Keep up the good work 👍

[@vintagelaph]

Sir, I do not know how to thank you! But you should know that you saved me and helped me a lot!! God bless your beautiful soul!

[@khalilhasan2004]

knowing which row to add so the other zeros stay the same is sill confusing, anyway this guy is saving my engineering career

[@seanhsieh4149]

Thank you for teaching us STEP BY STEP , I just don’t understand that why a lots of teacher they skip a bunch of steps like this, while they teaching NEW CONCEPTS.resulting students don’t even know how these answers come out…….😢

[@zappist751]

"a single mistake like that can be costly" bro this is why i hate linear algebra so godamn much D: I am literally sniffing my own fart to comprehend how in the godamn world this thing works. Thanks for explaining it haha I am in tears lmao

[@AG-cx1ug]

To do the reduced row echeolon form, is there a reason you went to make -1 at (1,3) 0 first? And then -3 at (2,3) and last 1 (1,2)?

[@salmanzaman7020]

When you search for matrix reduction and the first video pops up is of an organic chemistry tutor.

[@suman1272]

you pronounce "3" the same way my brother pronounces it. It's cute

[@M.A.H.I.R]

8 dislikes !!!!!!!!!!!!!! lmao you gotta be kidding me. wallahi (by God), this is one of the finest teacher I've came across ,thank you so much @THE ORGANIC CHEMISTRY TUTOR from bottom of my heart, May Allah swt bless you.

[@MonumentalDong]

why would u use Gods name for no reason like that u blasphemous rat

[@theadel8591]

diamond beatsx why don’t you stop insulting people and get yourself educated about people’s beliefs and cultures. Not all people are animals that don’t have any meaning in life other than work, sleep, eat like you, no there are people who believe in God and pray to everyday. They know why they were created.

[@MonumentalDong]

If you truly believe in God you wouldn't be using his name to emphasize how helpful s math problem is lmao that's just an insult to God

[@YellowGlitches]

@@MonumentalDong thanking God for receiving help from someone else isn't blasphemy. It's recognizing blessings, which we should do as it's not only respectful but kind.

[@celeryystick]

@@MonumentalDong L

[@rayiandelldcorpuz6111]

Bro I can't thank you enough! I'm literally in shock I just get it and I can't believe ittt.. my prof discuss this and I can't even understand anything he said you deserve my tuition broo!!!

[@liibaanxaashi8031]

I'm University student and this my assignment in university.Thank you so much for how helping me😊 🙏 .

[@beverlyfrancis8433]

Babes, I just discovered something. If you do the operations for the top right zeros working from the left, your proofs will be sure. THANKS A LOT FOR ALL YOUR HELP.

[@nightmarechameleon7502]

I've noticed some issues with actually doing the problems, so let me share what I've learned: In order to solve these, you need to generate zeros. In order to generate zeros, you need to generate ones, but that isn't too hard. Generating ones is easy, since all you need is an even and an odd number in the same column. If this doesn't work, you can also try dividing a row by a common multiple (E.X: 3 6 6 -> 1 2 2). When you have a one in a column, what you want to do is move that row to the top, then make everything below it a zero. Once you've done this, you can consider that row completed and column completed. The row because it has a 1 in it, and the column because it's all zeros. Then, you "shave" the completed row and column off the matrix and start again. Don't actually get rid of it, since you'll need it for the end result, and you might need the numbers to generate new ones.

[@mohammedabdiwalimohammed988]

You're expert really I watch all of your calculations also You're unlimited in mathematics sir . I have understood this well but it's necessary to find out it's formula

[@maimounah2001]

Nice explanation, it is so clear and easy you are really great teacher👍👍👌

[@JesusMartinez-zu3xl]

thank you so much!! you have gave me more confidence.

[@extremelightning6115]

Beautifully explained

[@jordanrichardson2367]

This interested me cause this lesson has my name in it :3

[@rmayr2075]

Aren't you not allowed to subtract R1 by R2 and then apply it to whichever you please? From what i've read the first row in the operation is the one undergoing the change

[@Rainonlandwhenneeded]

Can't be more thankful if that guy came and said 1+1=3 I'll believe him💙☁

[@landondursky2203]

This guy makes tough math look easy. Thank you!

[@romassamazhar2484]

I genuinely love you

[@Lolo-rq9ny]

Just a qq. At 6:40 you wote the matrix again but you wrote the Z as 6 instead of -6. Was that a small mistake or is there sth i dont get?

[@Lolo-rq9ny]

lol nvm. goated video

[@puterahaziman2205]

Thank you so much! First time learning this and thankfully got through the assignment well 👍🏻

[@ur_unrecylced_water_bottle]

Im in advanced math and im learning this and it is so complicated, this channel is the one i go to for this stuff

[@christianjullazarcon5071]

Finally find the right tutorial now i understand this lesson

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This guy is the best i have been struggling with this topic

[@Epicturtle007]

Thank you so much, very clear explanation of what my textbook made MEGA confusing. Pretty straightforward algebra when it comes down to it. Ill send you my degree in the mail

[@LexVexation]

This is so clear and rational, thank you so much!

[@ss-ev6pi]

"actually i made a mistake" forever calming 😅😅😂

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This video was really helpful,I hope I won't struggle anymore

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You are the best man! your teaching is amazing! you are an ingenious!

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you explained it better than my math teacher, ty

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My teacher tried to explain this to me a hundred times and I couldn't get it. I just got it with you! Keep up mate!!

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I think your teacher thought you DUMB!

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if there is a video from this channel that I didn't hit like button for, it means that I missed it.

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I swear i have an A in Linear Algebra this sem koz of you

[@haroonal-rasheed850]

hope I get the same result