Gaussian Elimination with Partial Pivoting

[@AFMathandEngineering]

Quick note, at roughly 3:40 you'll noticed that rows 2 and 3 swap. I pivoted them without writing down the step as I did the row operations. This is just to clarify any confusion as to why row 2 became row 3 and vice versa during this step.

[@loyisokhoali9511]

are you meant to do this or was this an error??

[@dantelutz206]

when you watch a video for help on that thing and they decide to just do the thing you dont know how to do XD

[@AFMathandEngineering]

Yea sorry about that :)

[@panosthunder643]

Why did you pivoted them? Don't you need to put the maximum value of each column, to the first row?@@AFMathandEngineering

[@unknownknown360]

@@panosthunder643 you actually need to pivot the 2nd and 3rd row int he following step. Because 3/2 > 5/6 and you need the bigger element to be at the top

[@akhmadjonovakromjon3669]

I like all of your Numerical Analysis videos. They are simple and great! Thank you for making a student's life easier! Appreciated!

[@AFMathandEngineering]

Thanks for the feedback!

[@okaudi]

So, Basically the meanign of Partial Pivoting is to switch the row which has the largest number to be the new first row, then using Guassian Elimination Method. Literally just adding the Partial Pivoting step to Guassian Elimination Method. is that correct understanding ??

[@Neuroleri]

This tutorial is short and precise! Understood perfectly

[@shahadabdullah1699]

THANKYOU LIFE SAVER, My final is tomorrow and its almost midnight, u really saved the moment thanks a lot

[@AFMathandEngineering]

Glad we could help you out, that's the main reason why we made this channel haha! :D

[@nahuel3256]

it'd be really cool to have some more videos on numerical methods :) The ones you made were really helpful

[@AFMathandEngineering]

Thanks alot, glad they helped! Well definitely look into making future numerical methods videos.

[@nahuel3256]

@@AFMathandEngineering thanks!

[@serden8804]

@@AFMathandEngineering exactly i am very excited to watch some videos about numerical methods from you

[@DJ-pn9te]

common techniques are to pivot off a row where the first variable has a coefficient of 1. Its not clear why you reorderd the equations in the first step. It would also be more clear that you change the row index identifications because you are not using the origianl rows coefficients.

[@amiramunirah955]

very helpful for my midterm examination coming soon. thank you!!!

[@lachydunne1512]

this is so much better than other methods, I was able to make a python function to do this

[@SS-in2kr]

Thanks for this video. I saw many videos regarding this, but only this video has the correct method of solution. My calculations kept getting messed up because of the faulty procedure in those videos.

[@mirjuniordochia3914]

thanks man, learned more in 8 minutes then in 10 years of math at school

[@syafiqh6382]

what if the column 1 have the same value? bcs we need to arrange it where the big value at the top right?

[@jrmath2003]

In that case, it doesn't matter which rows you swap

[@davidjnrananiawusah118]

thanks for your lecture. but pls after taking the highest absolute value to row one, does it matter if u interchange the other two rows left?

[@AFMathandEngineering]

In partial pivoting we don't exhange columns, only rows.

[@davidjnrananiawusah118]

I mean the remaining two rows

[@YashKumar-br5xi]

greatt buddy , but what is the use of finding pivot points in this method?

[@andressoto5935]

bro thank you. this was on an extra credit problem for my numerical analysis final and i got it thanks to you.

[@AFMathandEngineering]

That's what we like to hear haha, no problem

[@teresaileuk1513]

Could you help with a tutorial of steps of Gaussian elimination method when using multipliers

[@jc_hz4196]

super helpful thank you!!

[@elysonpanolino5413]

how partial pivoting helped?

[@Bravo-oo9vd]

watched the video to understand a meme, was not disappointed, thanks

[@hankerafterlaunchfahims7292]

Thank for the video,🎉

[@ivodalpuppo4939]

hmmm... I thought that using the pivoting method, at the end of the process you should have four matrices (PA=LU).. and then apply the forward and back substitution. Maybe I misunderstood?

[@GateCSE280]

Max absolute value can present in any column right? Or we only need to check for the first column?

[@SafetyLucas]

You need the max absolute value to be at the top of whichever column you are eliminating in that step. For the first elimination, you are only checking the first column, but in the second elimination, the max absolute value that goes to the top will be in the second column (in this video, the max absolute value is already at the top in the second elimination so he doesn't have to pivot again). The purpose of pivoting is to make the multiplier be less than one. Computers handle numbers by floating point values, which are more accurate with numbers valued less than one. Pivoting reduces computational error.

[@fullmoon6520]

Thank you for your easy explanation.

[@TanerSoyer]

Bro firstly thank you so much. But i dont understand one thing. You make pivoting only to the second equation. why didnt you do for third equation ?

[@AFMathandEngineering]

Taner Soyer no problem tanner thanks for the question. are you referring to the row swap? I made a note in a pinned post that referred to me just pivoting the rows in one step when I row reduced. Is this what you were referring to?

[@TanerSoyer]

I mean is: do not we have to take equation 3 to the 2nd order?

[@AFMathandEngineering]

Taner Soyer in the second step you do have to swap the rows 2 and 3. I did swap rows 2 and 3 I just did it in the same step as my row reduction. I should have mentioned that I was doing a row swap though. Hopefully this helps.

[@fffppp8762]

1/6 + (-1) =3/2?

[@laplacekowalski4727]

exactly, that's what I thought also

[@dimasfaiz236]

He swap R2 and R3 while calculating on his own without inform us -_- while it's does'nt matter to the result

[@num007agent]

I LOVE AMERICA beacause of your absolutely great lecture

[@ABSayysO]

What if on the first row we have two numbers of the same quantity. Say 1 1 0 How do we swap ?

[@insert_usernamehere]

What is row pivoting?

[@biggapoww]

The another useful part of the video part of the video 04:20

[@rabinbk5014]

Hey there, it would be better if the angle of your camera would be 90 degree,,

[@AFMathandEngineering]

thanks for the feedback! its pretty hard with the current setup that we have, but well definitely take it into consideration.

[@teresaileuk1513]

Thank you for the tutorial

[@solomonrazakntiri4301]

what did you do to the second row when multiplying it by r2+1/6r1

[@freelancingandgraphicdesig7426]

He missed a step..but answer is right...

[@freelancingandgraphicdesig7426]

When we chack pivot in 2nd column,,we swap the R² with R³ then that matrix will be obtained

[@ibrahimsalim3529]

Thank you 🙏🏻

[@wansyahiran11]

thank you soooooooooooooooo much!!!

[@baliullahmalik]

GOOD JOB I AM IMPRESS

[@syakirshahidan4742]

Help, I cannot differentiate partial pivoting and normal one

[@AFMathandEngineering]

Google answers this question fairly well, but the simple explanation is partial pivoting only pivots rows, while full pivoting pivots columns and rows. The difference is the accuracy of the solution and the computing power involved.

[@danialbinabdullah2704]

x3 should be 4

[@maxjappert]

I wasn't aware that Ben Shapiro did linear algebra.

[@sunflowerism]

Thankssss!!! ❤️❤️❤️

[@AFMathandEngineering]

No problem!

[@xMr3BxTV]

if column 1,1,1 , what your doing?

[@AFMathandEngineering]

If the first column is 1,1,1, just subtract the second and third row from the first to make the second and third entry zero. You wouldn't need to do any row operations for the first column.

[@krishnadas6832]

Thanks

[@AFMathandEngineering]

Krishna Das thanks for the comment!

[@alejandromichel9998]

Wrong multiplication when finding zeros

[@AFMathandEngineering]

Where?

[@APAP247]

AF Math & Engineering The 3/2 should swap places with -5/6

[@MonikaMonikaaD]

👌👌👍👍🙏

[@carsonritchey487]

you lowk sound like ben shapiro

[@farhan1571]

The results are wrong

[@hank3327]

Yes at 3:40 rows 2 and 3 swapped. This is very confusing. It would be better to correct it

[@tuur319]

or you buy a calculator that can do this, lol

[@AFMathandEngineering]

If they allow it into your exam go for it :)

[@tuur319]

Literrally saw that i don't have to be able to do it out of my head the second i finished this video

[@genericgaymergirl9876]

Why did you swap the first and second row at the beginning?

[@mazarinaabuothman2145]

right. I'm so confused. -6