Row Echelon Form of the Matrix Explained | Linear Algebra

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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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21 окт 2024

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Комментарии : 180

@WrathofMath Год назад

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! ru-vid.com/show-UCyEKvaxi8mt9FMc62MHcliwjoin Linear Algebra course: ru-vid.com/group/PLztBpqftvzxWT5z53AxSqkSaWDhAeToDG Linear Algebra exercises: ru-vid.com/group/PLztBpqftvzxVmiiFW7KtPwBpnHNkTVeJc

@academicstuff548 11 месяцев назад

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

@WrathofMath 11 месяцев назад

Glad to help - thanks for watching!

@PunmasterSTP 3 месяца назад

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

@academicstuff548 3 месяца назад

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

@PunmasterSTP 3 месяца назад

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

@Mohammadrga 9 месяцев назад

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 Год назад

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 Год назад

Glad to help - thanks for watching and good luck!

@kevinzebb 15 дней назад

Thank god, ty man. My teacher just throws a bunch of pictures and has a lot of little comments that clutter and confuse the slides. This was clean, simple, and straight to it.

@WrathofMath 15 дней назад

Glad to help, thanks for watching!

@onetoten9109 Год назад

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

@Surya_Kiran_K Год назад

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

@ziyayldz331 Год назад

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

@WrathofMath Год назад

Awesome - thanks for watching!

@mahichaudhari9718 Год назад

this cleared up the topic so much, thank you!

@sharonnoel2218 8 месяцев назад

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

@JakubMazur-v5s 8 месяцев назад

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 2 месяца назад

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

@kirin4244 Год назад

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

@SILE75 Год назад

What course are you doing?

@PunmasterSTP 3 месяца назад

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

@azayez 11 месяцев назад

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

@erasmusadventure 10 месяцев назад

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

@zion932 10 месяцев назад

While I'm studying this in my junior class😊

@tactixianchess1409 9 месяцев назад

@@zion932I have to study this as a Freshman LOL

@zion932 8 месяцев назад

@@tactixianchess1409 it was kinda tiring part.

@kafuibrendaam-frankamegavi1611 7 месяцев назад

😂😂😂

@MicahTonning 8 месяцев назад

Thanks for the video. It was super helpful.

@WrathofMath 8 месяцев назад

Glad it was helpful!

@shahdadpeykani7641 9 месяцев назад

Thank you, the explanation was so understandable and simple

@physicss6696 2 месяца назад

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

@WrathofMath 2 месяца назад

Glad to help - thanks for watching!

@user-Nagaraj301 17 дней назад

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

@WrathofMath 17 дней назад

Glad to help, thanks for watching;

@RishiVaish-ym1nr 14 дней назад

Thank you, sir!

@AZULA69 13 дней назад

My bro gonnah hipnotise us with those baby blues

@WrathofMath 13 дней назад

🔵 🔵

@Maggi_Malik123 4 месяца назад

u r outstanding in teaching Algebra

@WrathofMath 4 месяца назад

Thank you!

@niketkumar9949 11 месяцев назад

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 4 месяца назад

I have the same question.

@adwikat6109 4 месяца назад

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

@Mithun526 4 месяца назад

Easy and excellent explanation

@WrathofMath 4 месяца назад

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

@shikha-qz8qi 7 месяцев назад

Nice class sir

@julieye2260 5 месяцев назад

Thank you so much! I finally understood it.

@WrathofMath 5 месяцев назад

Awesome, thanks for watching!

@knowledgetrix2623 5 месяцев назад

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

@luluzha3777 11 месяцев назад

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

@WrathofMath 11 месяцев назад

Glad to help!

@heroshorts4612 10 дней назад

Why is d. in row echelon form? The fourth row has a leading 4

@adwikat6109 4 месяца назад

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.

@twitchy1871 2 месяца назад

You’re a saviour!

@WrathofMath 2 месяца назад

Glad to help!

@bola5671 Месяц назад

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

@aliefhasyani1324 2 месяца назад

thank you

@WrathofMath 2 месяца назад

Glad to help, thanks for watching!

@Pookie-dj7hv Месяц назад

Thank you so much from Myanmar 🇲🇲😭❤️

@WrathofMath Месяц назад

Thanks for watching!

@rishab8428 9 месяцев назад

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

@maelysbourry1041 7 месяцев назад

you saved my life for my tomorrow exam thank you

@WrathofMath 7 месяцев назад

Happy to help, good luck!

@kchege-y9z 11 дней назад

Thank you..

@EdmondOhene-dd5dj 7 месяцев назад

good explanation

@WrathofMath 7 месяцев назад

Thank you!

@Culturacept 6 месяцев назад

Thank you for this.

@WrathofMath 6 месяцев назад

Glad to help!

@henry_jem2126 20 дней назад

thank you sir

@punditgi Год назад

Nice video! 😊

@WrathofMath Год назад

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

@jadeistg 18 дней назад

THANK U SO MUCH

@WrathofMath 17 дней назад

THANK YOU FOR WATCHING

@beki-fl7hk 4 месяца назад

it was very helpfull tnx teacher

@WrathofMath 4 месяца назад

You are welcome! Glad it helped!

@ikeosode8744 Месяц назад

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 Месяц назад

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.

@gunboundmagFires 5 месяцев назад

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

@divyajyoti398 10 месяцев назад

Thanks bhaiya 😀😊

@nazrinnira3481 7 месяцев назад

Thank you ❤

@WrathofMath 7 месяцев назад

Welcome!

@upasanadas6883 Год назад

Thank you ... good explanation :))

@WrathofMath Год назад

Glad to help - thanks for watching!

@AnisubHindi 16 дней назад

Hey how do i get the notes of this video lectures?

@deveshsaini4959 Год назад

Thank you Brother

@WrathofMath Год назад

Glad to help - thanks for watching!

@_PowerPlay_55 9 месяцев назад

thanks mate!

@WrathofMath 9 месяцев назад

You're welcome!

@FranklineMawira-s1l Год назад

Wow thnks vry helpful.

@WrathofMath Год назад

Glad to help - thanks for watching!

@Hohoooooyyy Год назад

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 Год назад

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.

@rahulshendre7089 4 месяца назад

thanks

@karkilearning Год назад

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 Год назад

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 Год назад

@@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 Год назад

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!

@drisyasree 5 месяцев назад

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

@MikeMike-o7k 7 месяцев назад

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

@WrathofMath 7 месяцев назад

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

@divyanshkhanna8216 10 месяцев назад

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 10 месяцев назад

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

@krasimirronkov17 Год назад

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

@WrathofMath Год назад

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

@diyasehgal2413 17 дней назад

All properties need to be satisfies ??

@PunmasterSTP 3 месяца назад

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

@Merkolie 5 месяцев назад

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

@ANSvlogsBennettUniversity 8 месяцев назад

Love from India

@WrathofMath 8 месяцев назад

Thanks, love back from Cape Cod, USA!

@Snigkar Год назад

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 Год назад

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 Год назад

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

@shaikirfan8041 8 месяцев назад

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

@JakubMazur-v5s 8 месяцев назад

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

@rishiaman2288 8 месяцев назад

this was equivalent 5 lectures of linear algebra

@yashkashyap3887 10 месяцев назад

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 10 месяцев назад

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.

@poopeye09 7 месяцев назад

you make things so difficult

@Grostel018 6 месяцев назад

Lmao😂😂😂😂

@-NguyenVietKien-J 6 месяцев назад

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

@WrathofMath 6 месяцев назад

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?

@pterodactylboy1233 19 дней назад

“Each column containing a leading one has a zero in all its other entries” but example d does not qualify this

@Techno-Adnan 10 месяцев назад

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

@WrathofMath 10 месяцев назад

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.

@Benjamin-ex9pd 3 дня назад

@mohdarsh02 26 дней назад

can anyone please explain why why d and e part is in RREF form at 7:00

@WrathofMath 26 дней назад

1) Any rows of zeros are below all other rows 2) Every nonzero row has 1 as its leading entry 3) Each leading 1 occurs further to the right than the 1 in the row above it 4) Each column containing a leading 1, has 0s everywhere else

@rishiaman2288 8 месяцев назад

6:06 i still dont get why 4 is rref

@Minisynapse Месяц назад

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.

@bazmira3283 Год назад

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

@WrathofMath Год назад

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-seet9VyHo3Q.html

@wajeehalamoudi5945 Год назад

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

@WrathofMath Год назад

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

@garnachowoodutd 2 месяца назад

Which one is the anton textr

@WrathofMath 2 месяца назад

amzn.to/43xAWEz

@QuoteTrek 5 месяцев назад

What about d bro

@LO3. 9 месяцев назад

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

@adeoyeemmanuel4385 7 месяцев назад

Clap for yourself

@tdudejr55 6 месяцев назад

Homie graduated from Yap University 💀

@rahulshendre7089 4 месяца назад

@OceanDreams-xs1ii Год назад

e is not in RREF

@wajeehalamoudi5945 Год назад

i think same because 4th column contain 1 and 3

@JakubMazur-v5s 8 месяцев назад

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