Dr Peyam spoils us too much with this amazing content
@algorithminc.88503 жыл бұрын
Quite useful ... for performance computing and hardware development, always looking at how to keep integers until I have to use floating point ... Thank you ...
@AaronRotenberg3 жыл бұрын
Before you start trying to reinvent how to do high-performance Gaussian elimination with integers only, I recommend doing a fair amount of research... this is a _very_ well-studied topic. And it's easy to design pathological matrices that exponentially blow up the precision you have to store unless you use a clever algorithm - see rjlipton.wordpress.com/2015/01/14/forgetting-results/
@mayankshukla12743 жыл бұрын
It is a very good way to find the solutions of linear equations without getting fraction.Thank you sir
@gamedepths47923 жыл бұрын
This way too good to be true! This both saves time AND reduces mistakes which are extremely essential for competitive exams!
@bprpfast3 жыл бұрын
Yoooo now we need Dr K to be featured on this channel!!
@drpeyam3 жыл бұрын
We should!!!
@6754bettkitty3 жыл бұрын
When I first saw this, I was reminded of Cramer's Rule. I'll call it a hybrid between Gaussian Elimination and Cramer's Rule.
@GRBtutorials3 жыл бұрын
LOL, this was my first thought too. The proof is probably similar.
@LunaPaviseSolcryst3 жыл бұрын
I typically like to do an extra step where I find the LCM between the two numbers I'm trying to get rid of (so 6 for 2 and 3) then in the 2nd step I eliminate them by subtracting rows. It's more steps but each step I'm less likely to make a mistake since the additions between rows will always be by a factor of 1 or -1 and the multiplications ought to always make the two numbers the same, so I can check if the other entries were not multiplied correctly. The trick is to break down the problem into steps that your brain has optimized like -6 + 6 = 0.
@SlipperyTeeth3 жыл бұрын
I believe that this is effectively the same method. It just hides the multiply step and doesn't change the pivot row. Actually, yours uses the LCM, whereas this one just straight multiplies.
@MrCigarro503 жыл бұрын
Just amazing. I did not know this technique, but you have made my teaching a lot more enjoyable. Those fractions made me and my students going crazy.
@MuPrimeMath3 жыл бұрын
Wow, this is so cool!
@cyto33383 жыл бұрын
Gauss would really be proud, thank you for this amazing method !
@Justiin_rm3 жыл бұрын
that is beautiful. i wish i knew this when in mathematics class. thank you Dr Peyam.
@SlipperyTeeth3 жыл бұрын
The use of the determinant here seems like it might just be a coincidental shorthand. It will haunt me unless someone finds a generalization that uses determinants of higher order matrices. But I don't even have the slightest idea of what it would even have to generalize - Guassian Elimination itself?
@AaronRotenberg3 жыл бұрын
I think the algorithm in the video is just doing some shenanigans with Cramer's rule or matrix minors. Gaussian elimination will be exponentially faster than that for larger matrices.
@SlipperyTeeth3 жыл бұрын
@@AaronRotenberg I don't think you understand the method. Each entry only requires the determinant of a 2×2 matrix regardless of the size of the original matrix. Here is an explanation of the method I gave elsewhere: So you have a pivot row and a row you want to "update"; first, simultaneously multiply the pivot row by the first number in the "update" row and the "update" row by the first number in the pivot row; then, do the usual Gaussian Elimination on those two rows. What you've done is the simplest way to ensure that you get only integers in the rows, because now the number you want to turn into a 0 in the "update" row is the same in absolute value as the first number in the pivot row, so Gaussian Elimination amounts to adding/subtracting integers. At the same time, if you look at what you've done term by term in the "update" row, it's exactly the determinant described in the video, because you are just multiplying the respective terms by the first numbers in the other row before subtracting. I believe it is equivalent to standard Gaussian elimination in terms of computation time. If there is a connection to Cramer's rule or matrix minors, I would appreciate an explanation.
@theproofessayist84413 жыл бұрын
Now we need a proof presentation that this algorithm works!!!! :) - YAY hate making arithmetic mistakes with Gaussian Elimination!
@drpeyam3 жыл бұрын
The proof is easy, try it out
@edgardojaviercanu47403 жыл бұрын
I am astounded. A beautiful method.
@bigcheese68553 жыл бұрын
I'm about to take Linear Algebra starting this Monday. I have no clue what all of this is just yet but I'm saving this so I can reference it later on this quarter. Thank you, and great work!
@dr.rahulgupta75733 жыл бұрын
Simple and clear presentation. Excellent ! DrRahul Rohtak Haryana India has
@ahmedmghabat79823 жыл бұрын
Just after two days of following , you deserve subscribtion❤
@sharpnova23 жыл бұрын
just like you, i love the forward aspect but have no intention of that backwards component! i intend to implement this in code for fun. very neat trick. i think i understand why it works too. glad my linear algebra still feels fresh thank you for the great content and enthusiastic math, you're awesome
@cepatwaras3 жыл бұрын
this is awesome technique. I wish I knew it when in high school.
@stephsteyn46383 жыл бұрын
This is an excellent method! I wish I could use it in my linear algebra course but my lecturer requires that at each step I indicate which Elementary Row Operation was performed.
@bprpfast3 жыл бұрын
Wow!!
@shaycorvo42903 жыл бұрын
Wow thank you sir for this amazing technique....
@alvarezjulio38003 жыл бұрын
Oh Master Gauss look is awesome!
@paperpen57663 жыл бұрын
Impressionnant !
@sarkarsubhadipofficial3 жыл бұрын
Great sir❤️ Love from India
@mimithehotdog78363 жыл бұрын
4:22 Magic!
@jaikumar8483 жыл бұрын
Hello Dr payam ! Any trick or shortcut to find inverse of matrix?
@rikhalder57083 жыл бұрын
Smart handsome Guess 😂
@phat53403 жыл бұрын
Will you ever explain why this works plz
@LaerteBarbalho3 жыл бұрын
It's just the Gaussian Elimination with a factor to eliminate the fractions. Let's suppose you have a 2 x 2 system: a11x + a12y = b1 a21x + a22y = b2 To get a 0 in place of a21, by normal Gaussian Elimination, you multiply row 2 by -(a11/a21) and sum it with row 1: (-a11/a21*a21 + a11)x + (-a11/a21*a22+a12)y = (-a11/a21*b2 + b1), You can rewrite that as: 0 x + (-1/a21)*(a11*a22-a12*a21)y = (-1/a21)*(a11*b2 - b1*a21) and you just multiply by (-a21): 0 x + (a11*a22-a12*a21)y = (a11*b2 - b1*a21), and you can see the determinants right there. I'm no mathematician, but I hope I could help you.
@AlfonsoNeilJimenezCasallas3 жыл бұрын
Determinants are an interesting toolkit for solving linear algebra problems 😁
@yilmazkaraman2563 жыл бұрын
Nice one
@AriosJentu3 жыл бұрын
Interesting technique, but how about proof that this is works. I think it maybe not too hard to do, because it uses basic row-summing with common multipliers for rows, etc. Interesting, how they relates with determinant. Thank you.
@drpeyam3 жыл бұрын
No the proof is easy, try it out with a matrix a b c d e f And first row reduce, and then try this trick, and you’ll see it’s the same
@nathanisbored3 жыл бұрын
@@drpeyam does it have to be a square matrix (w/ augmented column)?
@drpeyam3 жыл бұрын
@nathanisbored No I don’t think so, it works for any matrix
@tambuwalmathsclass3 жыл бұрын
Dr. You are doing a great job. What name should we call this method?
@drpeyam3 жыл бұрын
Koster’s Method haha
@tambuwalmathsclass3 жыл бұрын
@@drpeyam 😁 Named after his name😁 thank you Dr.
@tzonic86553 жыл бұрын
I wonder if i can use this in my linear algebra finals
@drpeyam3 жыл бұрын
Sure!
@carlosgiovanardi81973 жыл бұрын
awesome!!
@carterwoodson88183 жыл бұрын
Does this method have a name? I feel like ive heard this referenced as montante's method?
@makavelix77673 жыл бұрын
I like your line which i believe 😊😊
@OssianDrums3 жыл бұрын
Lol you're a genius. I needed it, thanks!
@sanjayk96243 жыл бұрын
I like this method
@我妻由乃-v5q3 жыл бұрын
Great!
@rezamiau3 жыл бұрын
Absolutely incredible!! Does this method work with 4×4 systems as well ?
@drpeyam3 жыл бұрын
Yes it does!
@1willFALL3 жыл бұрын
Really clever technique, does this work for all three by three matrice? What about the inconsist case or infinite solutions, how would this work?
@nournote3 жыл бұрын
I guess you would find at some point a line with all zeros : 0 0 0 | 0 And in the case of 0 solutions, something contradictory like : 0 0 0 | a (a≠0)
@drpeyam3 жыл бұрын
It works for any kind of matrices
@lenamaral60553 жыл бұрын
Great 'trick'!
@dragonsdream4236 Жыл бұрын
This method is incredible but I am unsure as to how it works
@User-gt1lu3 жыл бұрын
69k not bad.
@JimmyCerra3 жыл бұрын
This is very interesting! I am taking Linear Algebra next term. Thank you! I have a question, professor. Does this work well with larger matrices? Or only systems of 3 linear equations of 3 variables?
@drpeyam3 жыл бұрын
It works for any system
@abhilashsaha45903 жыл бұрын
Amazing! But how does this method work?
@JoachimFavre3 жыл бұрын
It is just a regular Gaussian elimination, but by only doing multiplication. For example: (2 5 | 3) (6 15 | 9) (3 2 | 7) becomes (6 4 | 14) We multiplied the first row by 3 and the second one by 2. This way, you can just substract them. Dr. Peyam's method is exactly the same, just doing two steps at once, with a determinant. I don't know if I'm very understandable, do not hesitate if you have any question x)
@abhilashsaha45903 жыл бұрын
@@JoachimFavre Thank you I understand now.
@JSSTyger3 жыл бұрын
For me, calculating determinants is a tedious process because of having to remember minus signs.
@thanhliemtu80713 жыл бұрын
Can we also use this method to find the inverse of a matrix?
@thanhliemtu80713 жыл бұрын
Ok I came back here from the future and the answer is definitely yes
@jeemain90713 жыл бұрын
Thumbnail 😎😎😎😎😎
@MrCigarro503 жыл бұрын
Does this work for square matrices of higher dimensions?
@drpeyam3 жыл бұрын
Yes, and in fact for any matrix
@apoorvvyas523 жыл бұрын
Why does this method work?
@jamest86843 жыл бұрын
Great, but I fail to see WHY this works.
@vigneshshaik39883 жыл бұрын
He just applied row operations if u see clearly in those determinants
@jackiekwan3 жыл бұрын
2 1 4 |5 3 -1 2 |2 to take the determinants of first 2 rows is the same as to multiply the 1st row by the 1st element of the 2nd row (i. e. ×3), multiply the 2nd row by the 1st element of the 1st row , i. e. ×2 and then do the subtraction to eliminate the 1st element of the 2nd row the rest is done in the same concept
@chriswinchell15703 жыл бұрын
@@jackiekwan Well explained. It’s essentially a fast way of multiplying the rows by the least common multiple.
@berzerksharma3 жыл бұрын
I use 3d geometry to solve linear equations in 3 variables, will the society accept me?
@ethancheung16763 жыл бұрын
Cool technique but How does it work?
@drpeyam3 жыл бұрын
Try it out for a general 2x3 matrix and you see the pattern :)
@SlipperyTeeth3 жыл бұрын
So you have a pivot row and a row you want to "update"; first, simultaneously multiply the pivot row by the first number in the "update" row and the "update" row by the first number in the pivot row; then, do the usual Gaussian Elimination on those two rows. What you've done is the simplest way to ensure that you get only integers in the rows, because now the number you want to turn into a 0 in the "update" row is the same in absolute value as the first number in the pivot row, so Gaussian Elimination amounts to adding/subtracting integers. At the same time, if you look at what you've done term by term in the "update" row, it's exactly the determinant described in the video, because you are just multiplying the respective terms by the first numbers in the other row before subtracting.
@رضاشریعت3 жыл бұрын
I will kepp using cramer's rule even after watching this video anyway😂
@lenamaral60553 жыл бұрын
Check out the method of triangles.😉
@umerfarooq48313 жыл бұрын
Dr πM Math made fun and easy
@Jim-be8sj3 жыл бұрын
Better: A\b
@LaerteBarbalho3 жыл бұрын
I've found the engineer...
@Jim-be8sj3 жыл бұрын
@@LaerteBarbalho Close. I am in the applied math trade, but I teach engineers linear algebra and numerical analysis. It goes like this: A) Here's Gauss-Jordan, by hand. B) Here's LU factorization with pivoting, by computer. C) Forget what you know and use Matlab backslash. :)
@rjbeatz3 жыл бұрын
Hello
@jayeshyedge71713 жыл бұрын
Normal method is sufficient to do this question.
@SlipperyTeeth3 жыл бұрын
Are you sure about that? Computationally, integers and floating point numbers have different blind spots where they have to round. If given a problem in integers, converting to floating point might lead to unnecessary rounding errors.