Row Echelon Form of the Matrix Explained | Linear Algebra

We introduce row echelon form of a matrix, compare it with reduced row echelon form of a matrix, see several examples of reduced row echelon form matrices and row echelon matrices, and finish by using Gaussian elimination to transform a matrix into row echelon form. #linearalgebra
A matrix is in row echelon form if its zero rows are at the bottom, its nonzero rows have leading 1s, and each leading 1 is further right than the leading 1 above it.
Reduced Row Echelon Form Explained: • Reduced Row Echelon Fo...
Guide to Gaussian Elimination: • A Guide to Gaussian El...
Find Rank of a Matrix: • How to Find the Rank o...
Linear Algebra course: • Linear Algebra
Linear Algebra exercises: • Linear Algebra Exercises
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[@WrathofMath]

Support this course by joining Wrath of Math to access exclusive and early linear algebra videos, original music, plus the lecture notes used in my videos at the premium tier! kzbin.info/door/yEKvaxi8mt9FMc62MHcliwjoin Linear Algebra course: kzbin.info/aero/PLztBpqftvzxWT5z53AxSqkSaWDhAeToDG Linear Algebra exercises: kzbin.info/aero/PLztBpqftvzxVmiiFW7KtPwBpnHNkTVeJc

[@academicstuff548]

This Video saved me to a great extent in my Linear Algebra course.

[@WrathofMath]

Glad to help - thanks for watching!

[@PunmasterSTP]

Did you go on to take another math class after that?

[@academicstuff548]

@@PunmasterSTP yes had a prob & stat course after that.

[@PunmasterSTP]

@@academicstuff548 That's cool! How'd you like it?

[@Mohammadrga]

You are the best! In my algebra classes i just write the topic then or sleep or play with my phone. I don’t listen to the teacher, just search the topic.

[@newbie8051]

Ah, thank you for explaning this simple concept. Missed a few classes of linear algebra back in 12th grade and used to run away from linear algebra, Even had to revise matrix multiplication in my 4th semester as an ECE undergrad. We had a question on finding out rank of matrix in the midsem of an introductory course for Deep Learning, thanks for clearing this out sir !!

[@WrathofMath]

Glad to help - thanks for watching and good luck!

[@azayez]

why the hell am i studying this in 1st year bachelor of business administration

[@erasmusadventure]

Don’t worry….I’m in 1st Sem of masters…and I’m still stuck on this😂

[@zion932]

While I'm studying this in my junior class😊

[@tactixianchess1409]

​@@zion932I have to study this as a Freshman LOL

[@zion932]

@@tactixianchess1409 it was kinda tiring part.

[@kafuibrendaam-frankamegavi1611]

😂😂😂

[@onetoten9109]

Thanks so much for explaining. I was getting different answers when I didn’t do it a certain way 2:47

[@ziyayldz331]

Great video! I am an engineering student and this video helped me a lot, thank you.

[@WrathofMath]

Awesome - thanks for watching!

[@Surya_Kiran_K]

If you were my teacher I would never miss your class ❤️tqsm

[@kirin4244]

Currently taking a franken-class of linear algebra and multivariable calculus concepts with R. This cleared up so much confusion. Thank you!

[@SILE75]

What course are you doing?

[@PunmasterSTP]

Dang, that sounds like an intense class! What is it called and what degree are you going for?

[@mahichaudhari9718]

this cleared up the topic so much, thank you!

[@sharonnoel2218]

In the example(e.) is not in RREF ,because there is a 3 in the 4th column above 1.

[@JakubMazur-v5s]

But the 1 in the 4th column of 2nd row is not a leading one. The leading 1 of the 2nd row is placed in a 3rd column that doesn't have any non-zero values in it ;) Thus it is actually RREF

[@abood_rizing7018]

​thanks so much for explanation i thought the same as him@@JakubMazur-v5s

[@Pookie-dj7hv]

Thank you so much from Myanmar 🇲🇲😭❤️

[@WrathofMath]

Thanks for watching!

[@shahdadpeykani7641]

Thank you, the explanation was so understandable and simple

[@knowledgetrix2623]

Thanks sensei. I'm just a night here before the exam

[@user-zk9hs6yw5i]

Thanks for the video. It was super helpful.

[@WrathofMath]

Glad it was helpful!

[@physicss6696]

You are great ❤ ... Thanks for explaining this complicated topic so easily.

[@WrathofMath]

Glad to help - thanks for watching!

[@niketkumar9949]

Thanks for these videos.But i have question how d is in rref when last column has leading 1 but the other entry is 3?

[@mestawotmarimo849]

I have the same question.

[@adwikat6109]

exactly. I think he was wrong. you need to reduce the 3 to be 0 as well.

[@adwikat6109]

Great video! However, Regarding the last example, I think we need to reduce 3 to be 0, depending that we have a rule of all zeros except the pivot in any column.

[@Maggi_Malik123]

u r outstanding in teaching Algebra

[@WrathofMath]

Thank you!

[@bola5671]

Thank you good sir. My professor has a speech impediment (inability to share his information with his students efficiently or at all)

[@julieye2260]

Thank you so much! I finally understood it.

[@WrathofMath]

Awesome, thanks for watching!

[@aliefhasyani1324]

thank you

[@WrathofMath]

Glad to help, thanks for watching!

[@gunboundmagFires]

bro just skipped the boring part and gave us the ultimate explanation

[@Mithun526]

Easy and excellent explanation

[@WrathofMath]

Thank you! Doing my best to explain all of Linear Algebra!

[@twitchy1871]

You’re a saviour!

[@WrathofMath]

Glad to help!

[@maelysbourry1041]

you saved my life for my tomorrow exam thank you

[@WrathofMath]

Happy to help, good luck!

[@PunmasterSTP]

Row echelon form? More like "Really awesome videos; you're taking the math world by storm!" 👍

[@luluzha3777]

hiiii this helped a lot thank you sm for making those videos!

[@WrathofMath]

Glad to help!

[@EdmondOhene-dd5dj]

good explanation

[@WrathofMath]

Thank you!

[@shikha-qz8qi]

Nice class sir

[@Culturacept]

Thank you for this.

[@WrathofMath]

Glad to help!

[@beki-fl7hk]

it was very helpfull tnx teacher

[@WrathofMath]

You are welcome! Glad it helped!

[@rishab8428]

From where did you learn to explain? you're very good at it.

[@ANSvlogsBennettUniversity]

Love from India

[@WrathofMath]

Thanks, love back from Cape Cod, USA!

[@ikeosode8744]

g at 6:56 is in RREF. The -7 is not in the column with a leading 1. The 1 and -7 are in the same row not columns.

[@WrathofMath]

There is a leading 1 directly below the -7, this prohibits the matrix from being in RREF, for which it is necessary that all leading 1s have 0s above and below them. Note a leading 1 is a leading nonzero entry in a row. So we would not say the leading entry of row 2 is the 0 in column 1, but rather the leading entry of row 2 is the 1 in column 2.

[@Snigkar]

example 'e' at 6:16 is actually NOT a RREF right? because the fourth column has 3 1 0 0, so other than 1 and 0s there is also a 3. You said it's a RREF and my guess is that it's actually just REF :|

[@WrathofMath]

Thanks for watching and what I said is correct. The reason is that we only need 0's in columns with leading 1s. If a column contains a leading 1, all other entries must be 0s. But column 4 has no leading 1, does that make sense?

[@ethanborysewicz]

@@WrathofMathI had this question as well, thanks for clarification

[@punditgi]

Nice video! 😊

[@WrathofMath]

Thank you Ezra! Looking forward to building my Lin Alg playlist this year!

[@upasanadas6883]

Thank you ... good explanation :))

[@WrathofMath]

Glad to help - thanks for watching!

[@Hohoooooyyy]

9:53 so the final answer here is in row echelon form right? So if we need a RREF , we should convert that three into 1. Am i correct?

[@WrathofMath]

You are correct that the final answer is in row echelon form, that was our goal. To get it in RREF, we'd subtract 3*R2 frmo R1, to turn the 3 into a 0. Also, the second to last matrix we had (I might have said this in the video) is in REF according to some definitions which do not require leading 1s for REF.

[@karkilearning]

Love the video. However, I have one question. How is a zero matrix in RREF. Following rule #2 for REF, 'All zeros must be at the bottom of the matrix'. In example f, the first two rows are zeros, which should possibly violate rule #2 right? Thanks in advance!

[@WrathofMath]

Thanks for watching and for the question! By "at the bottom" we mean below all nonzero rows. For a zero matrix, every row is vacuously below all nonzero rows, because there are no nonzero rows. Does that make sense?

[@karkilearning]

@@WrathofMath That makes complete sense now, thank you so much! I'd just like to add that this is probably the *BEST* video out there to understand REF and RREF. Your video on Gaussian Elimination is also literally the best one out there.

[@WrathofMath]

Thanks so much! I work very hard to create the most clear and helpful video on each topic - so to know I reach that goal at times is a great compliment!

[@nazrinnira3481]

Thank you ❤

[@WrathofMath]

Welcome!

[@deveshsaini4959]

Thank you Brother

[@WrathofMath]

Glad to help - thanks for watching!

[@divyajyoti398]

Thanks bhaiya 😀😊

[@rahulshendre7089]

thanks

[@FranklineMawira-s1l]

Wow thnks vry helpful.

[@WrathofMath]

Glad to help - thanks for watching!

[@_PowerPlay_55]

thanks mate!

[@WrathofMath]

You're welcome!

[@rishiaman2288]

this was equivalent 5 lectures of linear algebra

[@divyanshkhanna8216]

In the last column of d part we have a leading 1 and other element is not zero, then how is it a rref?

[@WrathofMath]

It is not a leading 1 because it is not the first nonzero entry in its row

[@drisyasree]

4:22 in this section the the b) is rref . Can you give me the linear equations of this rref ?

[@Merkolie]

I still do not get the e because in the 2nd to last column, there was a 3 above the 1 and this means it doesn't satisfy the 4th condition

[@krasimirronkov17]

Will you make a video about explaining the definition of a determinant in depth

[@WrathofMath]

Yes I will - I will be working on lots of lin alg this summer!

[@tdudejr55]

Homie graduated from Yap University 💀

[@rahulshendre7089]

fr

[@-NguyenVietKien-J]

Can u pls explain again why f is a RREF bcs its fully 0

[@WrathofMath]

Two reasons 1) RREF has requirements about leading 1s. Since this matrix has no leading 1s, there is certainly nothing violating the conditions about leading 1s. 2) RREF requires zero rows to be "at the bottom" but more formally what we mean by "bottom" is below all the nonzero rows. So trivially this property is fulfilled also. Does that help?

[@MikeMike-o7k]

Its great But is it must that the leading entry be 1 for row echolon form ?

[@WrathofMath]

It depends on the author. Howard Anton's elementary linear algebra is the textbook for my playlist, and it requires 1s.

[@poopeye09]

you make things so difficult

[@Grostel018]

Lmao😂😂😂😂

[@adeoyeemmanuel4385]

Clap for yourself

[@yashkashyap3887]

d is not in RREF as 4th column has a leading 1 but other entry in 4th column is 4 instead of 4 so it is not in RREF

[@WrathofMath]

The 4th column does not contain a leading 1 because a leading 1 is a 1 that, in its row, is the first nonzero entry. Only columns 1 and 2 of matrix d contain leading 1s.

[@Techno-Adnan]

in d question we have a leading one in c4 but the other entry is 4 so how is it in rre form

[@WrathofMath]

Thanks for watching and for the question! C4 does not contain a leading 1 because the 1 in C4 is the not the first nonzero entry in its row. The first nonzero entry in its row is located in C1, so it is C1 which contains a leading 1.

[@shaikirfan8041]

in e example the 4th column contains 3 so that is not in row reduced echelon form

[@JakubMazur-v5s]

But the 1 in the 4th column of 2nd row is not a leading one. The leading 1 of the 2nd row is placed in a 3rd column that doesn't have any non-zero values in it ;) Thus it is actually RREF

[@garnachowoodutd]

Which one is the anton textr

[@WrathofMath]

amzn.to/43xAWEz

[@rishiaman2288]

6:06 i still dont get why 4 is rref

[@Minisynapse]

Same. According to RREF definition it is not RREF, because the leading 1 on the last column is not accompanied by zeroes evertwhere else, because the leading 1 is accompanied by the number 4. The rules seem to be very clear so it must be a mistake.

[@QuoteTrek]

What about d bro

[@wajeehalamoudi5945]

how could e. be RREF ? 4th column contain 1 and 3

[@WrathofMath]

Yes but it doesn't contain a leading 1, so it doesn't need to be all zeroes.

[@LO3.]

1:14 We don't care about what WekaPidEA said

[@bazmira3283]

Can you link the video to Gaussian Elimination please- can’t seem too find it in the description

[@WrathofMath]

kzbin.info/www/bejne/qZbIpWyMrq2iabM

[@OceanDreams-xs1ii]

e is not in RREF

[@wajeehalamoudi5945]

i think same because 4th column contain 1 and 3

[@JakubMazur-v5s]

But the 1 in the 4th column of 2nd row is not a leading one. The leading 1 of the 2nd row is placed in a 3rd column that doesn't have any non-zero values in it ;) Thus it is actually RREF

[@kongsjaj]

You look like carl of mr beast

[@KirubelDesta-je4ci]

you got one question wrong!!!!!

[@WrathofMath]

which?

[@KirubelDesta-je4ci]

@@WrathofMath nah sorry bro, i got it wrong myself, great video tho, i liked the video

[@ZorroNumber1]

Too bookish. I need more natural and intuitive.

[@mickeywebb6850]

extremely poor explanation TBH

[@cumfarthugetitties5265]

This video was uploaded 9 months ago, so it means that if a woman was impregnated during the upload must having a delivery while I'm writing this. This statement is accurate and the error could be of max few weeks

[@BetelhemAb12]

Thank you

[@WrathofMath]

You're welcome!

[@أبوالبر-و6ه]

thanks.

[@WrathofMath]

My pleasure - thanks for watching!

[@micahtonning7967]

Thank you

[@WrathofMath]

You're welcome!