Matrices: Reduced row echelon form 1 | Vectors and spaces | Linear Algebra | Khan Academy

[@Crunkmastaflexx]

Khan is the professor of every engineer, scientist, economist, and mathematician of the Western world.

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I swear this guy has a degree in literally every field possible

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whole world man

[@susmitasunar3921]

And east as well Here from south asia👍️

[@moserdaposer221]

I may jus give my college funds to mr khan cause i learn more in 10 minutes than i do in a week in my courses

[@longjili8139]

true story lol

[@oneinabillion654]

I agree. Its rare for math videos to be so thorough like Mr Khan's and fast as well.

[@abelgulbet1729]

College, bruh I am learning this in highschool

[@ovauandjahera8664]

@@abelgulbet1729 OMG! This kid!?

[@sounakroy1933]

@@ovauandjahera8664 we learn thisss in 10th grade. Your GCSE level.

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This guy is a million times better than all my other teachers...

[@ethan9435]

Agree. No offence to teachers around the world but we do need more people like this guy who knows how to explain in a way idiots like me can understand

[@fitjoe7]

@@ethan9435 lol, your reply made my day. We need more teachers like him. I hope you are doing good.

[@AmritGrewal31]

@@ethan9435 we aren't idiots, mate. Some teachers just use bigger words than necessary to say simple things to sound smart and feed their egos. Nobody is born a scholar, it is usually just about babysteps that those kind of teachers tend to skip because they rather be pretentious. I swear it really gets on my nerves.

[@TheRok]

12:56 I was following well, but it all went over my head from this point on. I'm guessing it's because I need to understand what vectors are first.

[@Zombl337]

Do you do math tutoring courses?! You tought this to me better than my professor or my college math book did! Thank you so much for helping me get a 100% on my homework this week :)

[@ducksducks2962]

wow 11 year old comment. How are you doing?

[@icem6765]

what wouldve been helpful is for him to explain how he made the decisions to use certain formula in the row operations

[@HappehLlama]

thank you so much. this was so incredibly clear and much better than my textbook.

[@KewlKid]

Having to do this at a level now this video has saved me

[@alirezasaf]

I wish you were my math lecturer, so I would not need to waste my time with my stupid lecturer. you are awesome.

[@Imac717]

Past my linear algebra midterm cause of you Sal! Thanks for all the help!

[@StaticShock1100]

@trinijenjen91 thats just how you do row echelon. Thats what you do, its another way of solving the equation.

[@DanesyaPratiwi]

to fill the second row, why do you subtract row 1 with row 2 but when you want to fill row 3 you subtract row 3 with 2 times row 1?

[@ayrtontv6025]

I cannot find on the entire internet a good explanation of what a pivot is

[@mikelim91]

i passed engineering with this, and now I'm back for a refresher!

[@nurmeshayusharrenasaifulla1937]

This being in my syllabus but my lecturer didnt teach this in class. Thanks mr khan for saving my life

[@gzimhasani4252]

Really helpful, one question I have is near the end. For the solution to define a plane, do we have to prove that the two directional vectors are linearly independent, and if so, how do we do that? (I know that creating a matrix where each vector is a column and showing that it's Determinant is not 0 is the method, but doing so does not create a square matrix so I can't find it's determinant?)

[@VangstaUNG]

Say negative 2 isntead of minus 2... It'd be less confusing

[@Numh2030]

when he mentions he already showed why there have to be leading entries and zeroes under them what video was he talking about???

[@keatongroom]

How does Khan know everything? So inspiring.

[@kvn89]

@zombiecarrot yes, as long as all 0 rows are beneath all non 0 rows

[@confusiouss]

Wish all lectures were posted on here, i could just replay it over and over till i get it :) thanx!

[@brandallbernal5924]

I understood everything but the pivot variable part.. Can you explain a little more why X1 and X2 were pivot variables ?

[@Revolut1on1ze]

I agree, the Internet is the most powerful learning resource. It helps to have an instructor to give you guidance.

[@AndrevMaverick]

this guy is a blessing, thanks a lot!!!

[@christina1495]

you explain it so much better than my linear algerbra professor. i wish i had you as my prof

[@zhijin0201]

Seems like hard n complicated, but still thx

[@iSolarSunrise]

This video + Some advanced linear algebra textbooks > Learning linear algebra in College

[@hugomsouto]

Unbelievable outstanding lesson, thank you so much.

[@S1CKDRIFT3R]

@yellotheemcee thats the standard form used in linear algebra, cos sometimes you can get matrices with such higher dimensions that its impractical to use different letters and makes it easier to keep track of using subscripts

[@brownie7535]

In first question you have applied R1-R2 into R2 which is violation of matrix rules . While iperating on Rn we can only do Rn -/+ Rm only

[@eiknas]

at 09.50 minutes into the video, i think there's a mistake. the 1 is supposed to be the only non-zero entry in the COLUMN. not row :)

[@JCP598]

One thing I don´t get, is the fact that you have the 1 in the second therm at position x3 and not x2. I thought you had to had the leading ones at the corresponding xi position, so the 1 on the first row is at x1, on the second at x2 and so on. Can you explain this point? Thanks by the way! You explain math way better than any tutor I have had in university. Greets from Germany!

[@anonymous9217w2]

too good, mai aapko badle mai ek chiz de skta chahiye toh batana

[@akashkumarmishra4827]

really soo helpful......

[@energysage9774]

Not sure if this will be useful to you but I've found that, for any math course, if you disregard the textbook 90% of the time and instead get a Schaum's outline and a Dover book on the topic, you'll do far better in the course. The dover books are like $5-$12 and the schaum's are like $10-$15. Just don't go that route if you need something very modern, since most of them are from like the 60's. The Schaum's for differential equations completely trivialized my course material.

[@Citizen_J]

@MrLilphill96 it doesnt have to be. as long as the next leading one is to the right, and down a row it is ok.

[@rachl_baegl]

bro everyone in the comments talking about this in a college course while im over here learning this in 9th grade alg 2 :/

[@TheMusa277]

you rocks.......you make math a fun......

[@LAnonHubbard]

I've watched every video in the linear algebra playlist prior to this one in order. I don't really get where this follows on from. The previous one was about dot/cross product intuition. I definitely didn't get the bit about the solution defining a plane in 4 dimentions!

[@ChimaevMikelson]

yes , i also searched if there is any glitch in the oder , but it is what it is.

[@ombatti]

thanks you've really plugged me

[@RichardLFG42]

at 12:34 ish you could have found all four variables based on those two equations. why didn't you?

[@ApplianceRepairOfTucson]

long but nice

[@szranger62]

how do u know when to change which number to 0 or 1? why do we need to change the '1' ( 1st row, 3rd number ) to 0?

[@amardadel5516]

it's like solving an equation by substituting and isolating one variable

[@ebisajaleta3235]

there are rule where to make 0 or 1. The first non-zero element in each row, called the leading entry, is 1. Each leading entry is in a column to the right of the leading entry in the previous row. Rows with all zero elements, if any, are below rows having a non-zero element. A matrix is in reduced row echelon form (rref) when it satisfies the following conditions. The matrix is in row echelon form (i.e., it satisfies the three conditions listed above). The leading entry in each row is the only non-zero entry in its column.

[@chinedusamuel7950]

Thank you so much sir for the lessons. U may not have any idea how much you are impacting people all over the world with these awesome teachings and explanations

[@anandib5401]

OMG! I was just 1 year old when this video was uploaded..

[@thelemur]

yeah, i know this method by "gauss elimination", and "row echelon form" is just a term that describes the zeroes and some of the conciderations regarding the 3 possible solutions: 1 sol, no sol and infinite sol. I think you should at least add "gauss elimination" in the search tags :) Good vid though!

[@ShivamPatel-hc8gk]

DAE have no trouble w/ multivariate calculus but hates linear algebra??

[@MontylsHere]

guys now i have a matrix i wan get the column echelon form.. what i did was.. that i got the row echelon form then got the transpose of it is that the column echelon form of the matrix? plz help me fast :D:D

[@Crayfish1010]

Man you are awesome!!!

[@konchokpenzila564]

really awesome teaching...keep helping us sir ...thank you ....

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This man has the best voice ever!

[@essojene4052]

chilllll

[@MGuD18]

Very easy to understand now, thank you

[@vaishakhsz]

tommorow 12 years happy birthday in advance to this video

[@arnoldxode]

Is there a specific way of solving this , like u gotta perfome this and after that or u gotta find your ways of reducing numbers to zero??

[@holmes4drums]

haha, I have got that covered to haha, have taken advanced english for the last 4 years. My iphone however, has some issues with it, haha. It corrects proper grammar such as you're to your, don't ask why. Nice catch though, lol.

[@a7medabdelsalam775]

at 4:34 should be -2 not to because u multiply by -1

[@colinmurphy2214]

He was subtracting R_1 from R_2. No multiplying

[@shrutisingh-x3p]

@@colinmurphy2214it’s still wrong tho

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God bless Khan Academy!!!

[@NLD1988]

For Khan-videos there should only be one button.. the LIKE button!

[@zombiecarrot]

will it still be rref if last 2 rows are 0 = 0 ?! or is it only the last 1 row that can 0?

[@12devilstriker12]

THANK YOU!!!

[@timyerboi]

wow thank you so much simpler

[@jamesbrowning7258]

So whenever I have more variables than equations, the first thing I should I automatically do is turn it into rref?

[@govou3000]

what if i decide to directly work with the linear equations ? is that gonna work? will still get the echelon form?

[@holmes4drums]

your doing this in college? I have to do it in highschool, lol, exam tommorow.

[@TheFaridzahin]

Around 9:50 the only non-zero entry in the row or the only non-zero entry in the column?

[@thelemur]

isnt this basically gauss elimination? Reduced echelon form is a product of carrying out the gauss elimination, right?

[@sarathy319]

Just a small query : For full rank 3x3 matrix whose rref is identity matrix , Then how this reduced Identity matrix will help me in computing the solution AX=B ..coz i would be getting the values of X as same as B for all square full row matrices.Please correct me if iam wrong

[@santoryu8940]

Around 4:20 how did u know that u must subtract the second row by the first row?

[@ibayanx3410]

areesetotle he wanted to get that 1 into a zero. there are some rules that you can follow when you're doing the reduced form. 1) switching rows. 2) multiply a row with a nonzero number. 3) addition and subtraction between two rows. note that we can't multiply two rows together but you can multiply a row with a number and then add it to the other row that we want to change.

[@santoryu8940]

thanks for the explanation

[@ibayanx3410]

areesetotle no problem 😊

[@Wrathos]

Whenever I read up on the rules, subtracting rows was never mentioned, only adding them together. This created alot of confusion. Even the Matrix Row Operation rules listed on Khanacadamy doesn't state this.

[@hutto969]

thanks mate

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I LOVE KAHN

[@abhilashshakya8511]

Simply awesome.

[@tahniafarheen4636]

GOD BLESS YOU MY BROTHER!!!

[@14Truthfulls]

Thanks for the video. Is nice to refresh memory, i took Linear Algebra about 2 semester ago. And forgot most of the stuff i learned. Your video is great refreshing memories. :)

[@Breadbeecp]

Can you solve it without vectors?

[@travisl6654]

But what if you didn't know you could turn one of the numbers to a 0 or one and you end up with a row that you thought was a free variable. Would that change the final answer?

[@joeljoemathew]

I understand u better than my prof :D keep up the good work

[@macmorten1]

@TheZketch lol no it's smoothdraw

[@mr_toy_emporium5990]

Great video

[@snapphanen]

It's 1-(-1) = 1+1 = 2

[@b3nsh4]

Awesome

[@Fatalsh0ts]

better than my 6 grand tuition;.....

[@josephtetteh1562]

Honestly I still don't get it. So what's the valve for x1, x2, x3 and x4?? Please..

[@aminesahsah2050]

in your first example how come 4-2*2 is equal to zero

[@mido9545]

I figured it out, he does the multiple first, the subtraction is latter.

[@renreccion1042]

thank you!

[@SalvationTobela]

Can we have two or more pivot entry in a row?

[@colinmurphy2214]

Salvation Tobela no

[@Mirroredsmoke]

upper echelon

[@mamaliga_cu_lapte]

How can someone unlike this

[@trinijenjen91]

how come u are minusing 2x row 3 from row 1 and putting that as your new row 3??

[@yalnayal]

thank youu♡

[@ashtonscalise6949]

can anyone tell me why he made this 1 a zero at 7:55?

[@izzy2129]

i thought this was row echelon form not reduced row echelon form

[@alexkonopatski429]

I have a question about the pivot and free variables. Can someone pls explain to me, why x_1 and x_3 have to be the pivot variables and not x_2 and x_4. Or can I just mix them as I want to, because it doesn't seem to have any relefance. If it has to do with the pivot entrires, then why? Why do these 1's tell us that x_1 and x_3 have to be the pivot variables (I understand that it is because the first row and third row mark the x_1 and the x_3, but why are the 1's so special)? I really hope someone could anwser me, 'cause that would really help Thanks in advance!

[@23Foxford]

Im wondering how can you solve it, if the equations are equal to zero. Basicaly i have a problems when one or more coeficients are uknons too. And in one of these all of it is equal to 0.

[@gunslinger123456]

very helpful, love it

[@gaurangisrivastava781]

Thanks a loooooo...∞t!!!

[@TheMalaysianInvasion]

Can someone tell me why 3x4 is not a free variable?

[@s0m0c]

X4 is indeed a free variable no mater what coeficient is in front of it.

[@zoommo]

thank you very much @student in Thai

[@SwagatMahapatra16]

adobe beta Love Thailand and Thai People ❤

[@timetime89]

im also watching it for my matrix class as well 5555

[@zoommo]

thx ♥

[@kristoffers.andersson8263]

At about 11:10 is x4 in row 1 also a free variable? Or is it that only one x4 can be the free variable?

[@10181995hamza]

x4 is a free variable so whichever line its written in it will still be a free variable hope that makes sense (:

[@kristoffers.andersson8263]

Thanks, think I ment to ask if there can be several answer to one unknown.

[@kristoffers.andersson8263]

:p

[@woodenjaw]

Holy Cow!

[@maven12LA]

I need help. I was trying to find the rank of the matrix, I use echelon reduced form and my rank answers are correct but my reduced form matrix is different to the solution. How many reduced form echelon matrix are there? Just one or many possible reduced form matrix?