Row reduction, row-echelon form and reduced row-echelon form

Row reduction, also called Gaussian elimination, is the key to handling systems of equations. We go over the algorithm and how we can make a matrix fairly nice (REF) or very nice (RREF).

[@bonaboiz718]

This is GOLD. Education would be no big deal if you had a video like this for all type of technics.

[@jasrindersingh5836]

this was a 100% better explanation than my finite professor, thank you

[@Picklejar75]

best explanation on youtube, wish i has seen it earlier.

[@iamyiyaj646]

very helpful! I love how you explain the rules in the beginning first instead of just going into it like everybody else. I was confused on how to know what operations to actually do in the rows and you helped with that

[@jakobpind]

HI Lorenzo. Just wanted to thank you for explaining it, so even I can understand. Had it in class today, and it made zero sense to me. Now i get it. Thank you very much!

[@tessacortes9226]

Thank you so much. This is so much clearer than my textbook and class.

[@sasidharrathnam2057]

Seriously this is the best explanation I've got through youtube. Thanks again..

[@fadedthanahoee]

Thanks for the explanation. Have an exam tomorrow, this helps a lot!

[@SEEKINGKNOWLEDGEMIND]

Best explanation, even better than my teacher

[@themustangmachine]

This is a great explanation! Thank you for explaining this in a clear and concise way!

[@maazahmedpoke]

PIVOTTT! PIVOTT! PIVOT!

[@BayAreaChill]

this video is underrated in so many ways

[@amosfondo9940]

This is so wonderful. Everything is well explained, love it!

[@JaimeHernandez-hx8xe]

in Min 3:15 why the substraction is equal to 3 i thought it will be -1 , I am taking about the 2 row and the 2 item of the row which originally was 1.

[@enamulkarim8735]

thanks a lot sir ....for making it so easy...my teacher's explanation was the worst..i had to say...LOVE FROM INDIA

[@junohara1713]

Hi Lorenzo. Covid lead me here. I like your paper with David Auckly, and have cited it several times. It's nice to know your great activity, both in research and education.

[@mehanaziqbal5434]

You're a life saver!

[@ahlem4217]

First thank you for this explanation it's really useful ! it's just that I don't understand how the 2 in the first row just became 4 (??)

[@trillonairesclub2329]

woow i can t leave without a comment THIS IS VERY AWESOME THANK YOU GOD BLESS YOU

[@ihebhaboubi1570]

i couldn't understand it until i watched this video , thank you

[@skittles6486]

Very good and simple explanation. Thank you

[@GurpreetKakar4873]

Best explanation on TH-cam. Thanks very much.

[@lovealter4246]

hello, sir. Thank you so much. really helpful to understand difference between ref and rref!!! thank you so much!

[@anandahlawat7967]

Thank you so much for the perfect explanation

[@barretttoups6496]

I like to enter the matrix into my Casio 9750 and then use the RREF tool to determine the solution.

[@abhishekjayesh3517]

this man is blessed

[@SauravKumar-mp7xb]

best explaination sir,great

[@userozancinci]

so nice and clean

[@fridge8416]

Such a great explanation!

[@jakobkall]

It is in rref, but there is no solution to the system, because of the third row right? 0=1, which is false

[@Ahmad-dk8uu]

Tysm you saved my quiz

[@DhananjaySingh-ff2zg]

Can we just divide 2 and 3 from 1st n 2nd row respectively directly..i mean wouldn’t we take 1/6 outside the matrix?

[@Quealberta]

so is the number two on the second row a pivot or what is it? Im talking about the near end of reduce echelon form.

[@retrorinto929]

a doubt sir could u write on the right side while making rref what u r doing (example r1_r2)

[@vihangiiddamalgoda3948]

Best explanation. Thanks.

[@micah2501]

What a hero. Thank you!!!!!

[@Maggio97]

What do you do if the numbers are not easy multiplied or divisible ?

[@Generatorman59]

So, the final system of equations is: x + 4z = 0, y + 2z = 0, and 0 = 1. You don't see a problem with 0 = 1? What am I missing?

[@madhupramod]

The last column of the matrix is not right side of the equation. It's part of the equation with 4 variables (or dimensions) So we can have w + 4y = 0, x + 2y = 0 and z =0 and 0 = 0

[@darthJ9]

Generatorman59 how are you even generating a system of equations here? A is just a matrix it’s not equal to anything in the form AX=B for you to assume variables x y z w and equate it to a solution matrix

[@emmachang4807]

same here!!!! this would have no solutions?

[@julias5782]

this goes into classifying if the matrix/system is inconsistent or consistent. It a clue, towards earlier definitions and properties associated with the behaviors of systems

[@graju2000]

How do you say that this is an augmented matrix? only if it is an augmented matrix we can get any physical meaning out of it right..? Also if at all it were an augmented matrix the system doesnt have a solution

[@aamoddixit2441]

superb explanation

[@MohammedHussain-wu8gc]

im here because my professor uploaded powerpoints and reads over the problems instead of doing any of the work. #2020onlineclasses

[@shadmanbishal1333]

Best best explanation , Clear one

[@qaiseriqbal2696]

Thank You so much ...this help me a lot Sir .

[@Techjai000]

on interchanging rows a change in sign convention occurs you didnt mentioned it

[@jananisreeganesh]

Could we also say that rank of this matrix is 3?

[@AMOATIFA]

Very good explanation.. others were just confusing.

[@markjacinthtadle7714]

Why can't my professor explain this as simple as this

[@sepehremami9893]

thank you man...it was PERFECT

[@pratikbansal867]

Can echelin form be used in 3*3 matrix ?

[@aqibshah9234]

Excellent teaching method

[@spencerkaup2850]

Great video, helped me out a lot

[@justwasuploaded]

Thank you for your explanation sir!!

[@kdipapa7521]

Sir while adding 1st and 3rd row ,how does the 3 in the 2nd row gone

[@larissacollins9797]

thanks king!

[@abhirambulusu4405]

Thank you!

[@zulfaqaradli5826]

boek dokk✊🏻

[@ganeshavula7722]

i dont undertsand how you used subtraction because it isn't one of the three matrix operations?

[@lorenzosadun565]

Sure it is. You're allowed to add a multiple of one row to another. Subtracting B from A is just adding (-1) times B to A.

[@ganeshavula7722]

it works for the first row column(-2+2=0) but then (-10)+4=-6 not 6?....and (-7)-(-2)=-5

[@saharacarecenter2585]

video cleared me. thank you

[@danieldey]

That was very helpful. Thank you

[@rivayadav5805]

Thanku.. Sir ☺☺

[@NehaGupta-nz4ol]

Nice explanation ..

[@Quealberta]

thanks for impartial explanations

[@faheemullah5574]

thank u sir

[@chunsheng4578]

hi does the pivots in RREF must be 1??

[@sushilgyawali787]

thank you sir.

[@purnachander1563]

1000
0100
0010
0001 sir it should be in this form
But in the 3rd row it is 0001
Can we do this

[@ambikaponsuyambu5934]

Nice explanation

[@astleaugustin7748]

Owsm

[@Lakshybanking78]

Perfect explaintion

[@tobiasit2190]

that was beautiful

[@tessema8470]

shouldn't we have a leading 1

[@alijavdani292]

as far as I can see, in the 3:30 there is a mistake,
the row should have been (0,5,6,10) , and this changes everything.

[@hoomanjafari4633]

Thanks...nice work

[@firstpenguin5653]

Thx u made my day

[@Hiraofficial_]

thank you....

[@robsonmapfuyanzara5530]

Much appreciation

[@Soumya65]

Thnx man for helping out

[@muhammadluqmanal-hakim876]

What's pivots

[@ajithshetty9889]

Sir thought well

[@lalaland8602]

Thank you SO MUCH

[@michaelkievits7073]

your last row is incorrect, it should be 1 - (-4) = 5

[@kingkong4468]

Thank You!

[@archismanchakraborty8228]

First non matrix must be 1

[@Engr.Duceysane]

thanks bro

[@nimnanilwala5245]

Thank you sir

[@priyankashah8242]

it would had been better if the voice gets louder

[@chetanreddy106]

Lovely...!!!!!

[@YoganBarrientos]

Thank you

[@muddassirnazar9275]

Wow superb explanation... listened to khan academy video... absolute shit...but ur explanation is better than khan academy

[@dr.anishrituraj558]

Thankyou💐

[@nurilyana5747]

Dont understand

[@mirandoo300]

22.05.2020

[@mycousins896]

you are wrong. In REF the first pivots should always be ones. Below should be zeroes and above you dont care which number there is

[@Ds7nike]

POP

[@mannyjacobo8499]

pop

[@prachisikarwar3567]

Hindi bol lo toh hame bhi samajh aa jai

[@eda7210]

Thank you sir