Reduced row echelon form | Lecture 11 | Matrix Algebra for Engineers

How to compute the reduced row echelon form of a matrix.
Join me on Coursera: imp.i384100.net/mathematics-f...
Lecture notes at www.math.ust.hk/~machas/matrix...
Paperback at www.amazon.com/Matrix-Algebra...
Subscribe to my channel: czcams.com/users/jchasnov?...

[@ProfJeffreyChasnov]

Find other Matrix Algebra videos in my playlist czcams.com/play/PLkZjai-2Jcxlg-Z1roB0pUwFU-P58tvOx.html

[@arthurquinton4932]

I dont mean to be so off topic but does anyone know of a tool to get back into an instagram account??
I stupidly forgot my password. I appreciate any help you can give me!

[@arthurquinton4932]

@Kamari Leonel I really appreciate your reply. I got to the site through google and im in the hacking process now.
I see it takes quite some time so I will reply here later with my results.

[@arthurquinton4932]

@Kamari Leonel it did the trick and I finally got access to my account again. I'm so happy:D
Thank you so much, you saved my ass !

[@kamarileonel1276]

@Arthur Quinton You are welcome :)

[@Coachizz-rf1kw]

@@arthurquinton4932 Guys dont follow these replies, they are bots, they are scamming you, BEWARE!!!

[@nadyaperezmartinez4251]

Thank you, definitely feel ready for my pop quiz tomorrow! :)

[@jayagarwal1934]

sir i am very amazed by the tech u are using

[@jivikabhat4645]

thank you so much my textbook didnt explain it like this added weird steps and made it super complex, YOUR EXPLANATION IS FANTASTIC!

[@abdulshaikh2401]

The way he introduces himself at the last takes my heart✨

[@idellius7505]

Very cool video. Thanks Jeff! 👍

[@melatonyea5284]

best video for explaining rref on internet!

[@teeheeeee]

you're such a *great* teacher

[@annoyingprecision2487]

Thanks! That was extremely helpful.

[@georginikoloff9280]

very neatly explained, thanks!

[@geoinformaticszone]

The bestband precise explanation

[@justbracefaceYT]

Thanks so much for this

[@terencewright2223]

Thank you ,excellent video.

[@kiruhbhavan6284]

it is a very amazing explanation. I quickly understand thank you, sir.

[@faresalouf]

Amazing video, how do you make the writing thing ?

[@gilangmaulana3731]

very understanable, have a nice day

[@rutujaroyals652]

Very helpful. Thank you Sir.

[@user-el1rg5ky7x]

well explained sir. congrats

[@mr.danielwizard.5890]

Good appreciated this

[@jamsonsamuel1776]

The best teacher

[@scann563]

this video was great. i also loved your performance in whiplash

[@Saidait0101]

😂😂😂

[@user-db9ie1bq4s]

Thanks Jeff, helped alot

[@wakuliradenis8903]

thanks for the lesson

[@blessedanopaishetsiga388]

THANK YOU SO I FINALLY UNDERSTAND

[@saeedataei269]

great teacher

[@gopukalatillinigopugopu7372]

Sir I understood. Thank u

[@saisusmithasanniboina3191]

Sir I like your teaching

[@Maths_love745]

I like you explanations sir

[@muzammalshahbaz7511]

Nice method

[@yasserhamdy5504]

thank u so much prof

[@nurulfadillah1248]

thank you!

[@zawnaing344]

thanks Dr.

[@andrewthebladethrower8371]

videos are not linked, I don’t see lecture 12. Otherwise, very good presentation. Though, this special case of zeros probably better introduced in other lecture?

[@snehamartin996]

Thank you sir

[@Karan-oo3zs]

Thnx sir,,,,,,,,,,, I'm from India🇮🇳🇮🇳🇮🇳

[@deisor]

Thanks.

[@FatmaHashim-bq7bo]

Thanks 😊

[@mitch2890]

where did he get the first -4 to multiply ?

[@abhishekmishra5645]

thank you sir i am from India

[@dervisdurmaz3497]

Sir, I think you should title your videos with the order of numbers. Otherwise, it is to difficult to determine which video is the next video. Best Regards. You are awesome btw.

[@ProfJeffreyChasnov]

If anyone wants to watch the whole course, either go to Coursera (I recommend this) or download my lecture notes "Matrix algebra for engineers," and use the links inside to watch the videos in order on CZcams.

[@pragathhis8412]

hey! can you please tell me when do you learn this in your years of school, like do you learn about this in collge, if yes can you please tell me which year of college are you learning this. Would really mean a lot if you replied, cheers!

[@ProfJeffreyChasnov]

@@pragathhis8412 Second year of college in a matrix algebra, or linear algebra course.

[@pragathhis8412]

@@ProfJeffreyChasnov thank you, I'm learning this is high school lol

[@Himani2112]

@@pragathhis8412 first year second semester

[@SamuelBardi]

1 question: if you only needed the very first column to be 1, why then did work on row one again?

[@desaikeyur5291]

GOOD EXPIRIYANCE

[@me2831]

Wish you mention what the solution is after doing all that

[@jalanelamessa1697]

Thanks

[@jpodumakwuiwu5813]

good day sir
you started with -4R1 + R2
can i say 4R1 - R2 and will i arrive at the same answer as you ?
please answer me

[@abson1408]

Ty

[@lianagilbert61]

But wait, is he facing the camera while writing all this backwards and right to left? What is this magic?

[@shreyasdas5130]

nah the video is just mirrored using software

[@weisanpang7173]

Hi professor Jeff, is rref used to find the solution for vector (x,y,z), like what the Gaussian elimination procedure does ? If yes, the resultant rref of the matrix A is a matrix with row 1 having the coefficients of the X1 and X3 terms, while row 2 has the coefficients of the X2 and X3 terms. If that's the end rref form, how do we find the answer for x,y,z ?

[@weisanpang7173]

Never mind, I figured it out after watching other videos of echelon form of matrices. Basically X3 was a free variable, which means there are more than 1 solution to the system of equations. In other words, substituting X3 with any numerical values yield different answers for X1 and X2.

[@curiousseeker3784]

would someone please tell me when should we interchange/swap/switch two rows?

[@ProfJeffreyChasnov]

By hand, when the pivot is zero or you can make the arithmetic easier. By machine, you also swap in the row with the largest in magnitude value of the pivot.

[@essieho]

Hi Prof. Chasnov, after watching this video, I attempted to answer the following matrix given by my university.
1 3 -2: -3
0 1 5: 9
0 2 3 : 4
The question is “ circle the entry which represents the pivot”. According to the official answer, only the leading entry in row 2 is the pivot. The leading entry in row 1 is not a pivot. Why is that?
By the way, I am a graduate of the business school HKUST in 2002, currently pursuing another degree with the University of London. Unfortunately, explaining questions to students is not the strongest link of the folks here. Thus, I need to seek a second opinion from a world class institute. Many thanks in advance

[@ProfJeffreyChasnov]

I guess row one is finished. So they want the pivot on the row that you are about to use in the elimination procedure.

[@sudarshanv9797]

This matrix has determinant zero, it has infinte solutions or no solutions at all, if it is System of linear equations

[@kaitlyndunn4571]

how did you divide 20 by 5 and get 2? 3:56

[@na3em303]

I just don't know when to multiply the first row by the second, or if I add or multiply the two rows by a any number and provide them with a second row or any row, this is my problem

[@devngecu]

At the begining,why -4 and -6?

[@bengrant9316]

How u get minus 12 ? I’m so lost

[@vinayas7644]

👍

[@MWENDA-vv5im]

2 school drop outs disliked this video.

[@yousifhanna4740]

You think you’re funny dumbass

[@asmasm182]

هلا بيكم طلاب قسم الرياضيات 👍

[@sirisha7747]

Your teaching is very good but it used to be easy to understand if u written row operations more clearly

[@CardiganBear]

Great video, thanks. There is a mistake at 03:58. When dividing row 3 by -5, the result should be (0 1 4 3), not (0 1 2 3).

[@ProfJeffreyChasnov]

I divided the row by -3.

[@CardiganBear]

@@ProfJeffreyChasnov Sorry - I misread the -10 on row 3 as -20. My bad!

[@aayeshaashfaque6437]

@@ProfJeffreyChasnov no sir you divided the row 3 by -5 and your calculation is right in the video

[@boachieyiadomgodfredfosu9494]

@@ProfJeffreyChasnov the guy isn't wrong. Look at where you divided by -5. There was supposed to be 4 and not 2.

[@camileclere8925]

why do we need to eliminate the 2 in step 3? when we have column 2= 2, 1, 1. You make the 2=0. Why is that?

[@ProfJeffreyChasnov]

definition of rref

[@domgesh392]

What is the meaning of pivot .....please explain sir

[@ProfJeffreyChasnov]

The pivot is the matrix element one uses for the elimination step.

[@domgesh392]

@@ProfJeffreyChasnovthank you sir 🙂

[@DeborahKhimbini-zx6cs]

-20÷-5 = 4

[@user-bs5jm5ob1q]

-3÷3=-1 why just 1????

[@INDIAN-uf2nz]

#savesoil

[@osenigoodnews4339]

What do we do when the pivot is not 1

[@akashbhandary3799]

Y do we have to multiply can't we just minus 4 in 2nd row?

[@salvindsouza7053]

Is dividing by a constant allowed? Isn't that only multiplying?

[@ProfJeffreyChasnov]

Yes, of course.

[@Paaxl]

Dividing by 3 is the same as multiplying by 1/3

[@user-oo2qg9go3l]

i love you

[@muhammadtanzeelhussain6121]

Sir where you live in city

[@jeromebantillan6399]

Why it is -2? Sir?

[@Harrysof_]

Thank you Jeff bezos !

[@ndagireangel5923]

20over5is4not2

[@ProfJeffreyChasnov]

True. What time stamp?

[@FBcrayz]

@@ProfJeffreyChasnov I think he/she is referring to the -10 in the third row but it is a misread. It's not 20, it's 10.

[@viperous3245]

Where is the last result

[@PapaJohnsPie]

*wait a second*

[@PapaJohnsPie]

i honestly *really* what

[@Abrar_Ahmad.]

Watching in 2024🥰

[@user-yn1fs3uq2j]

jeff bezos is that you ?

[@sabhiyakhatoon3710]

Jhonny sins 🤣🤣🤣

[@sudhanvaurs4007]

thank you!! That was well explained
!

[@ziadhossain9793]

Thank you sir