Gauss Jordan Elimination & Reduced Row Echelon Form 

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-4VAXv6yRULU.html

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.

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.

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!

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

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

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

I should stop going to class and watch these videos.

@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.

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

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.

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

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.

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

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.

Just want to let you know you're amazing! Anytime I run into challenges, I'm always stoked when your videos pop up. Thank you for all of your help!

This guy got me through highschool. Absolute legend

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

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!!

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

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

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

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 🙏

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

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

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 😭🙏

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

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🤣

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

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

you’re the goat of youtube my man

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

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

Көп рақмет! From Kazakhstan! much love!

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

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

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

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.

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

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

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.

This man has saved so many professors' jobs.

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.

This monk really helped me for my bachelor's degree

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

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

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

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!

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

I genuinely love you

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.

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.😍

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

Beautifully explained

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!

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

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.

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

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?

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

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!!!

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

This guy makes tough math look easy. Thank you!

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

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 RU-vid 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.

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

You are the best professors sir

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

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

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

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

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.

thank you sir !

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

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

THE HERO. YOU SAVE MY LIFE

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…….😢

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.

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

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

you are the best

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

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.

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

Nice explanation sir, thank you

I am so glad that I had this lecture before I take an exam!

Finally find the right tutorial now i understand this lesson

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

Thank you for your video lessons teacher !

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.

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

Who knew that adding and subtracting could be so hard

this was really helpful thank you so much

you explained it better than my math teacher, ty

You just made this lesson way easier for me. Appreciate it!

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

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

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

This man got the power of all my professors and TAs combined.

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.