Gauss Jordan Elimination & Reduced Row Echelon Form

[@TheOrganicChemistryTutor]

Matrices - Free Formula Sheet: bit.ly/3UE9Cmk 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

[@rebozone]

you didn't really described the reduced echlone form

[@kimsabo9597]

099999990999oo9oo0o99999m,,999999|00|

[@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.

[@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

[@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

[@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.

[@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

[@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

[@xPradeep_D]

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

[@ZavianN11]

Literally just commented this, thanks alot!!

[@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.

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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

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

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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

[@lekemorfaw237]

@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.

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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 😊

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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!!

[@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

[@tamiawilliams4761]

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

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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.

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@@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

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simp

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

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Good luck!

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I love your presentation. Normal speed, clear step and simple to understand

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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

[@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.

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[@PavanKalyan-bo6qp]

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[@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

[@Mel-f6w]

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?

[@Mel-f6w]

@@asadfarrajhey, I actually graduated college so I’m good, thank you

[@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 :-)

[@pamelakalimukwa4871]

I came from an online Harvard class on linear algebra that was making zero sense to me, now I get it, 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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I am a student of National University of Bangladesh .Really you convince quality is totally awesome.....tnx a lot my teacher .

[@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 😭🙏

[@LuisCunha-xn9vx]

I have a test today 😅

[@Ntchindi_N]

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

[@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🤣

[@alinahussain4842]

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

[@Exousia_TV]

😅😅😅

[@cemtolgamunyas4530]

same

[@InverseCr0wn]

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

[@Benedict_Miriti]

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

[@khalilhasan2004]

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

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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 👍

[@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.

[@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.

[@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

[@darlene506]

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

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Көп рақмет! From Kazakhstan! much love!

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

[@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

[@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

[@idaliihernandesss924]

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

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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.😍

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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 monk really helped me for my bachelor's degree

[@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!

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I genuinely love you

[@823studios]

This man has saved so many professors' jobs.

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this guy is just insane!

[@techboyvinny1024]

I never believe I could understand Gauss Jordan before a day to my exam, thanks a lot I really appreciate your videos

[@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!!!

[@idealmathsdeosir9308]

Thanks

[@HeroDw-n2m]

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!

[@rengiekago1850]

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

[@danielperezrosales8392]

You are the best professors sir

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

[@franco6380]

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

[@iancarlos9185]

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

[@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!

[@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

[@hizokadarkwolf]

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

[@Rainonlandwhenneeded]

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

[@LexVexation]

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

[@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

[@JesusMartinez-zu3xl]

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

[@maimounah2001]

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

[@landondursky2203]

This guy makes tough math look easy. Thank you!

[@extremelightning6115]

Beautifully explained

[@javineboltzmann4126]

Nice explanation sir, thank you

[@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

[@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.

[@suman1272]

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

[@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.

[@steliosgkelis1517]

You saved us bro, love u

[@richmondsam7776]

Man you're the best!!!!!!!!make it look easier God bless you

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

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[@JinxiLiu]

THE HERO. YOU SAVE MY LIFE

[@MrProgrammer69.]

The video shows how to use Gauss-Jordan elimination to solve a system of equations with three variables by converting it into an augmented matrix and performing row operations to obtain the reduced row echelon form. [00:00] Gauss Jordan elimination is used to solve a system of equations with three variables - The problem is converted to an augmented matrix - Elementary row operations are performed to obtain reduced row echelon form - The values of x, y, and z are obtained from the resulting matrix [02:39] Performing row operations to convert matrix to reduced row echelon form - Multiplying row 1 by -2 to get a leading 1 in the first column - Adding 2 times row 3 to row 2 to get a 0 in the second column - Adding -3 times row 3 to row 1 to get a 0 in the third column - Adding -4 times row 3 to row 2 to get a 0 in the fourth column [05:17] The video explains how to use row operations to make certain numbers zero in a matrix - To make a number zero, apply an operation on the corresponding row by adding or subtracting it from another row - Rows two and three can be made the same by adding them together - A mistake was made in the video, where a number was copied incorrectly, leading to an incorrect calculation [07:56] The video explains how to convert a matrix into reduced row echelon form - To convert a matrix into reduced row echelon form, apply operations to rows - To make the first number in each row equal to one, multiply each row by a fraction - The resulting values can be used to solve for the variables in the system of equations - In the example given, the solution is x=6, y=-1, z=-2

[@ZainCodeLab]

Watching this 1 hour before exam 😅😅😢

[@gingerbreadcat3165]

Who knew that adding and subtracting could be so hard

[@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

[@karl1751]

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!!

[@PavanKalyan-bo6qp]

I think your teacher thought you DUMB!

[@MFuhaid-x8s]

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

[@SeriousStudent603]

1:09 diff b/w row echelon & reduced row echelon. we make zeros frm top to bottom starting frm 1st column. actually, no. 8:04 . 4:05 .

[@philipchinweuba6511]

Thank you, you've made my day

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

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you explained it better than my math teacher, ty

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

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