Gaussian Elimination & Row Echelon Form
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- Опубликовано: 6 июл 2024
- 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.
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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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His exapmles are ass though. He picks the easiest examples. He could give a harder one.
@@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…
@@droomahbroo9291 i mean he could give one hard example. He chose easy examples. Ones i can easily do in my head.
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Textbook is pretty much a piece of brick
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Y’all are learning this in uni? Bro I’m having a hard time understanding this and I’m a freshman in hs
@@amreenaym786 just keep going, keep practicing. things will make sense eventually
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@@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
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can i minus 2 rows ?? someone answer plz
@@youssefbayoumi2694 What exactly do you mean? You can indeed add a row with minus 2 times another row.
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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
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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
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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*
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.
Thanks
@@taekwondotime so whats the scale operation
You should have explained that in the video I was so confused :(
The one he did is called Reduced Row Echelon form.
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!!!
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
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A THANK YOU COMMENT IS NEVER ENOUGH TO YOU GUYS!!!! LIFE SAVERS!!! THANK YOU VERY MUCH TEACHER, THE ORGANIC CHEMISTRY TUTOR.
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.
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.
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Currently stuck myself.
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same
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Simple, clear, and self-evident. Many thanks!
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You corrected both z=2 and -2 in the top row. Great job and thank you! I can solve variables using Gaussian elimination.
Thank you for writing that he caught that! I was getting worried lol
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Thank you for the vid! Explained it far better than my instructor did!
We have an exam tomorrow, including this topic. Hoping to pass it.
I have one tomorrow too cri.
@@neilialopez7446 ahahaha me too
updates? how was it! im having one soon :)
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 :)
ruclips.net/video/nyWp9sr8uGE/видео.html
UPDATE??
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They always do the easiest question on the internet.
well you only need the basic anyways for this kind of question.
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Otherwise we could be afraid of how difficult it may be : )
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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
thanks a ton mate
Thanks man now i think i understand.
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
@@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
@@oimatesimro2088 wouldn't R3 = -R1+R3 work then?
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Get more on Gaussian elimination method of solving systems of equations from this link
ruclips.net/video/eXHOytiWWAw/видео.html
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Linda in the UK
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Get more on Gaussian elimination method of solving systems of equations from this link
ruclips.net/video/eXHOytiWWAw/видео.html
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Get more on Gaussian elimination method of solving systems of equations from this link
ruclips.net/video/eXHOytiWWAw/видео.html
Passed my math exam coz of you. Thanks a ton :))
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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.
Bro it straight up WORKS. You gotta like a video that can explain A-Level maths to a 14 year old.
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)
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?
@@inarvii8181 correct
i finally understand! thanks!
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I learned this back in Middle School, but I forgot this was of doing it. Thanks.
found it easier than my tutor explaining, awesome
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same
can i minus 2 rows ?? someone answer plz
Damn this video is life-saving!
Thanks so much for this video
Very simple and clear
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Thank you for this ,
I have an exam
And this so diffcult for me
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Now i understand
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Wow u explain it in a simple way. Keep it up