Gauss Jordan Elimination & Reduced Row Echelon Form
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- Опубликовано: 4 окт 2024
- 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
Final Exams and Video Playlists: www.video-tutor.net/
Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections
Next Video: ruclips.net/video/4VAXv6yRULU/видео.html
Thanks for the help my g
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.
well...the test is after 2 hours..
It’s 2 hours before the paper 😢
Me rn
@@suheyl-hx6sh lmao same
literally me rn 2 hours before my exam rmfaooo
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.
Bro you saved me thank you so much
Nice 😮
Legend comment. Never know what direction to take the questions in.
What do you mean by pivot?
@@jd2981I think the number in the row/column that u want to change
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!
i am still confused as to how make this unholy disgusting garbage of a method to work
@@maindepth8830 Yup.
I’m literally in tears now typing this :(
@@mm-ol6ed appropriate profile picture
@@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.
My professors always explain things so fast I get hopelessly lost. You take your time to explain all the operations and I appreciate that
bro get your brain checked
bruh got me through Calc 2, now he's helping me in Linear Algebra, hopefully man dem have vids for Calc 3.
yup
his calc 3 vids helped me so much
Guy has like every stem subject covered for you
You got linear algebra after calc 2? No wonder i’m finding this so hard, i haven’t even done calc 1 yet
@@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
I should stop going to class and watch these videos.
Tyrell Harris I said the same thing yesterday!
i started doing that 2 years ago and I've maintained solid grades doing so, he's very good at explaining all math concepts.
Me too👌
No! Go to classes and watch videos. Do both, be more successful.
Yeah Uni is kinda a scam
My professor makes this seem so complicated but when you didn’t it was so easy.
he is ma sumperstar
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.
@@meanmole3212 idk man, if you cant introduce a topic to your students in a way that they understand then youre still a bad teacher
@@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
simp
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.
@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.
bro this is not music class to put instruments in you. go and study.
@@PavanKalyan-bo6qp You clearly don't understand simple english, i'm sorry for you
@@charless__10 who asked?
@@PavanKalyan-bo6qp I asked
@@PavanKalyan-bo6qpThat's the point no one cares about your opinion and no one asked 😊
It seems so easy until you try solving one question 😭😭😭
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@@abdomenebadellah
Does the order of finding the zeros matter? Do all zeros in this order before 1 right
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
For auto solution of gauss jorden method you can watch this tutorial to.
Thnx me later
ruclips.net/video/vzn85dJUf3M/видео.html
My teacher just linked this video for reference, a true G
Good luck!
I'm a university student, and your videos help greatly to my lessons Thank you🌼
Then quit University!
@@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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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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Go watch marvel.
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.
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.
I do this too!!! It’s so much easier for me
Thanks a lot 🙏🏻
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
Literally just commented this, thanks alot!!
I never believe I could understand Gauss Jordan before a day to my exam, thanks a lot I really appreciate your videos
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Who knew that adding and subtracting could be so hard
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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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same
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Who asked?
@@PavanKalyan-bo6qp i did
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THE HERO. YOU SAVE MY LIFE
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How you holding up now?
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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.
He is taking (R1-R2) and saving the result into the second row
This video was really helpful,I hope I won't struggle anymore
you explained it better than my math teacher, ty
Can't be more thankful if that guy came and said 1+1=3 I'll believe him💙☁
This is so clear and rational, thank you so much!
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!
Bro my teacher confused me with this, thanks for the clarifying what needs to be done first
Computer Science Linear Algebra gang where are you
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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!
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Thank you for your video lessons teacher !
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.
Very well explained, thank you
Thank so much. I almost forgot this question
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Thanks for this king
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 RUclips 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.
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Teacher at 5:53 u did a mistake because u wrote (3R1--R2) so we must change R2 not R1
"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
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you pronounce "3" the same way my brother pronounces it. It's cute
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