Dimension of the column space or rank | Vectors and spaces | Linear Algebra

Dimension of the column space or rank | Vectors and spaces | Linear Algebra | Khan Academy

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15 жыл бұрын

Dimension of the Column Space or Rank
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Пікірлер: 115

@matthewfedoseev580 2 жыл бұрын

"The rank of a matrix is the number of linearly independent column vectors that can be used to construct all of the other column vectors." Perfect. Thank you so much!

@andy121232 12 жыл бұрын

These vidoes make linear algebra so much more clear. I am always lost trying to decipher my teachers lectures and the text, but then i watch these vids and it all makes so much sense! Thank you !

@nereaelizaldeojembarrena450 5 жыл бұрын

You explain in 10 minutes what my teacher could not in two weeks. Thank you for saving my grade :)

@acadoe 4 жыл бұрын

At the time this video series came out, all people thought about was that it was great and that it explained things better than university professors, which allowed people to pass. In the future though, these videos will be considered as strong evidence for why in person university education is obsolete. These kinds of series will be the new basis vectors for education ;)

@CCCOBI 13 жыл бұрын

you just taught me in less than 13 minutes, what my prof failed to teach us for the past 2 weeks. Thanks alot to take time out of your daily life to help out students, especially for free.

@debarshiroy2939 2 жыл бұрын

thank you so much Sal Khan, though you released this more than a decade ago, these videos are still as useful and relevant. a BIG THANK YOU!

@brammattens1463 2 жыл бұрын

Facts

@ian.ambrose Жыл бұрын

Math will never be irrelevant.

@ibrahimkhalil5303 9 жыл бұрын

Thank you sooooo soooooo much, you are much better than a loooooot of profs in my university

@kaliberto1 5 жыл бұрын

I passed this class in college, and idk how did I passed it, but I came back for engineering grad school, and you have saved me!!!! This is supposed to be material I should've already known to understand more advanced topics :/

@verelanz 11 жыл бұрын

i love you, man... this is the first time i really understood everything someone told me about this stuff

@thevadidekizambak 12 жыл бұрын

that video will definitely help me in my final exam tomorrow. thank you!

@juanfelipe8484 3 жыл бұрын

This is so crucial. I’m thankful

@loredelfayer.areieta85 8 жыл бұрын

Perfect!! Thanks so much.

@Maverick.42 2 жыл бұрын

dim(null space)=number of non pivoted columns where as dim(column space)= number of pivoted columns. very nicely explained thank you

@hahaeliz 13 жыл бұрын

I have a linear algebra exam tomorrow. It's hard and I don't have a good prof and my text book is written in such a way that you have to unscramble what they are trying to get at... The guy I was paying to tutor me was terrible. I don't know why I bothered with all of that when you make something that seems SO FOREIGN so like, normal and not that hard! Your videos make me like linear algebra! (kind of... that might be an exaggeration) but THANK YOU SO MUCH FOR SAVING STUDENTS EVERYWHERE!

@jamesd9215 8 жыл бұрын

Thank you so much for this!

@phdcsc3383 3 жыл бұрын

Great Video! Thank you!

@pyakurel123 12 жыл бұрын

I donate some to khan .. So that this incredible work will not stop in future..

@dmurphy1515 8 жыл бұрын

I hope that you know that you are the reason i graduated!!!! haha at U of I to say the least you come in clutch and i can actually understand what your saying

@ishansrt 7 жыл бұрын

You are simply charming.saved my quiz day. Thank you

@georgechisanga 14 жыл бұрын

thanks for making "ranking" easy for me to understand,

@musabahmed3341 2 жыл бұрын

Best math teacher of all time!!!!!

@jaakkokuu 14 жыл бұрын

very helpful!

@EDMYuki 6 жыл бұрын

Thank you so much! :D This was so helpful!

@jamesandresen5971 5 жыл бұрын

Who else is watching this 10 mins before their exam?!?!!?

@ecoman003 2 жыл бұрын

Welcome to the club😂

@abhinandanbhardwaj1369 Жыл бұрын

Still you had time to type here.. 😁😁

@khaledsakkaamini4743 6 жыл бұрын

THANKS SAL YOU ARE LIFE SAVER

@shamrick6276 Жыл бұрын

this video lecture help to learn to basis , rank and dimension for the subspace of column vector which i did not find a good one anywhere. thank you

@kanupriya21 6 жыл бұрын

Thank you so so much!! xx

@splendidninja1378 10 жыл бұрын

Thank God for Khan Academy.

@macman592 6 жыл бұрын

thank you mr Kahn. you are doing Gods work my good sir

@Hfils 13 жыл бұрын

Good job !

@MrBassie123456789 11 жыл бұрын

Sir, you are awesome!

@abdulmagedkhaled9480 10 жыл бұрын

You save my life , thank you so much .

@emreer196 10 жыл бұрын

thanks a lot , that helped me a lot before my final !

@jefffan6379 3 жыл бұрын

thank you so much, your lecture is sooooooo great!

@err3088 4 жыл бұрын

Thank you much! That was really helpful! :)

@michaelt9266 4 жыл бұрын

Best video on youtube for this topic

@garcezvanessa 10 жыл бұрын

thank you!

@vikitanayak3771 8 жыл бұрын

thanx u r just amazing

@scottySK 15 жыл бұрын

thanks for making linear algebra easy, i wish my lecturer could explain things as simply as you do

@prabuddhmathur9941 2 жыл бұрын

must have been a great experience learning online in those days.

@justicedavhana9298 11 жыл бұрын

Thanx I find it helpful :-)

@SupreetSinghsuppi 4 жыл бұрын

Thank you so much!

@kohaku102038 13 жыл бұрын

thx..i've been reading about the rank and i don't understand at all... thx 2 u i understand it now

@migbadrule 12 жыл бұрын

THANK YOUU!!!!!!!

@rohanuplekar 14 жыл бұрын

thank you !!!!!

@pendawarrior 4 жыл бұрын

Thank you.

@user-lg7tl8rx2w 3 жыл бұрын

thanku so much!!!!

@PKDana 11 жыл бұрын

K I watched some videos, and I think it's what I said, except you do not go back to the original un-reduced matrix to find the linearly independent rows that comprise the basis for the row space of A: you just use those rows you found in the reduced form. Nicely, once you find the row/column space, it is an easy task to find the column/row space, since the reduction exposes both in the matrix.

@Loljdk 14 жыл бұрын

thanks man

@shahrukhkhalid5727 6 жыл бұрын

To calculate Col A, do u use echolon form or reduced echolon form, watching some videos on it and every video has different method. Some are using reduced and some echolon only. So im getting confused which one is supposed be used?

@thalassatrinculo 6 жыл бұрын

in this lecture you said dimension =number of pivot columns in c(A) however in the previous video called dimension of null space and nullity you said dimension= number of non pivot columns in N(B) so which one is it? # of pivot or # non pivot columns? or does that change based on if its a null space V.S a column space? and what is the difference between the two?Thanks.

@crazyidiot101 11 жыл бұрын

if you, patrick jmt, and thenewboston, and other like that were to open a college....your education would be way more valuable than any other college because the kids coming out of your college would actually know stuff

@Krisipoke 13 жыл бұрын

I really love your videos, they are awesome. You explain things much better than most of the professors in my university. Thank you very much. Although, you made a small mistake at 4:45. You said minus one plus minus one is zero and minus two plus minus two is also zero. Well, the second minus one and the second minus two were actually plus one and plus two. And minus one plus minus one would be minus two, not zero. :)

@AlexBaller134 7 жыл бұрын

thx

@Juliusblue 13 жыл бұрын

amazing... my linear algebra final is next tuesday. I only wish I knew about this throughout the whole semester. I bet I ace it with this help.....

@rubenramirez8062 4 жыл бұрын

Juliusblue Did you pass the exam?

@gddfhjiufcv 6 жыл бұрын

what if two pivot columns are the same in reduced row echelon form? Is the rank then 2 if you have 3 pivot columns as two are linearly dependent?

@hoomansv 13 жыл бұрын

ur perfect

@yaelba 11 жыл бұрын

When you rref the column space (or span), don't you have to like turn the columns into rows first and THEN go ahead and do the substractions? (And then turn the rows back to columns)

@Zoku012 10 жыл бұрын

Hey Sal, thank you so much for all your videos. So, pivot columns are always linearly independent right?

@realBenjaminFranklin_ 10 жыл бұрын

Yes, the set of pivot columns will be linearly independent. Think about it this way: what makes a set of vectors linearly independent? A set of vectors, A, is LI iff the only solution to Ax = 0 is the trivial solution (i.e. x is the zero vector). So, no linear combinations of vectors in A will equal 0 except for the case 0x1 + 0x2 + ... + 0xn = 0. By definition, a pivot column has a leading value and all entries underneath it are zero. So in the matrix: 1 0 0 1 No matter what nonzero scalar c1, c2 we multiply each of the vectors by, we will never be able to get a nonzero value when we add the vector components together.

@9BYN 12 жыл бұрын

you are awesome

@maledivennixe 10 жыл бұрын

Omg i love you!

@lazzuuu21 6 жыл бұрын

THAAANKK YOUUUU !!!!

@lebplayer004 12 жыл бұрын

do you mind putting better tracability on your videos so we can know which one is the next one

@MegaBdboy 7 жыл бұрын

So can we directly calculate the rank of the matrix to find the dimension and the linear independent vectors ?

@Rjsipad 6 жыл бұрын

yup

@JeromeSqualor 12 жыл бұрын

u are da bossss! im gonna ace my test tmrw!

@celeryystick 4 жыл бұрын

Nathaniel Sarkissian did you ace it? Lmaooooo

@renatomendoncaYT 13 жыл бұрын

Thank you for your videos! Very helpful. Also, the dimC(A) = Number of columns - caracteristic of (A) = 3 :)

@khusainovkhusniddin5820 4 жыл бұрын

Hey, can u reply me

@vinesteel 10 жыл бұрын

I start to realize that Khan is much better than my prof.....

@kanupriya3695 5 жыл бұрын

I can truly relate ✌

@jeroenvandekamp4656 5 жыл бұрын

11:30 for dimension, your welcome

@gabrielchase7729 6 жыл бұрын

are dimension and rank basically the same thing?

@sonianoviango 12 жыл бұрын

what is the difference between the dim. of subspace and col. space ????

@niroshas1790 6 жыл бұрын

may I know which text book u follow please

@thetravellerfeeds 4 жыл бұрын

How to figure out which the pivot column

@vasicnikola7674 5 жыл бұрын

i love you khan

@Liaomiao 11 жыл бұрын

so the dimension of the null space = # of pivot variables of the original matrix and the dimension of the column space = # of non pivot variables?

@MrSuperDagangsta 9 жыл бұрын

This guy sounds like WoodysGamertag. Great vid.

@jackgrothaus2722 6 жыл бұрын

WTF i was literally thinking about that yesterday and I haven't watched woodysgamertag in years

@anirudhsharma3879 3 жыл бұрын

Does span of column space define the space of vector space?

@d4ny36 13 жыл бұрын

@g1tfisted My thoughts exactly. My linear algebra teacher gave us all a take-home test that we have to turn in in two days, and no one really understood his explanation of column space and nullspace. Thank you so much for your help, this will surely help me answer some questions on my test. :P

@7ammada80 13 жыл бұрын

THANKKKKKKKKKKKK YOU SO MUCH . PLEASE PUT MORE AND MORE VIDEOS. EXPLAIN A SLOWER AND AT THE END OF THE VIDEO SAY MISPLAY WHAT YOU DID . JUST LIKE WHAT YOU ASIDE AT THE END OF THIS ONE. MORE AND MORE VIDEOS PLEASE

@solnary923 10 жыл бұрын

thanks! and I wished my bald , boring professor take some notes :p

@jstrong151 12 жыл бұрын

why is the 3rd column not a pivot entry

@sadmemeboi 8 жыл бұрын

6:50 dont you mean column 4?

@PaulMayeul 6 жыл бұрын

no, the pivot column has to have only zeros and one 1

@jeroenvandekamp4656 5 жыл бұрын

yeah he meant 4, you know its true

@oscarwahlstrom9476 10 жыл бұрын

Hello Khan academy, you have left me extremely confused since by the theorem of linear independence: If a set contains more vectors than there are entries in each vector than the set is linearly dependent. I must have misunderstood you so in other words: are you saying that the subset of A(a1, a2 , a4) is independent or that A (a1,a2,a3,a4,a5) is independent?

@niroshas1790 6 жыл бұрын

ya I too have this doubt

@2011bini 13 жыл бұрын

two people teach linear algebra. Sal and the guy who disliked this video.lol

@luisnazareth9193 3 жыл бұрын

so i can say, dim(C(A)) is equal with rank(A) ?

@werya85 15 жыл бұрын

I feel your pain!

@bigchunk1 14 жыл бұрын

Column space is column rank?

@wyphonema4024 7 жыл бұрын

so .... rank is nullity?

@shafiqhussainofficialmathe861 7 жыл бұрын

No! nullity is the dimension of the null space while rank is the dimension of the column space

@nati22 12 жыл бұрын

1 person needs to work on their clicking accuracy

@TCHRacoon 13 жыл бұрын

ah I should've skipped right to the end but the rest of the video wasn't too bad to watch either.

@nandanrohit7848 3 жыл бұрын

Why does he sound like Tom Hanks, lol?

@alepov 11 жыл бұрын

No, it doesn't matter. There is no "one right way" to rref a matrix, you can do whatever you want.

@RelativelyHostile1 11 жыл бұрын

lol same apart from I have to pay even more :(

@angela1894 14 жыл бұрын

I still don't understand what a column span is

@junkeychan 12 жыл бұрын

@lebplayer004 khanacademy [dot] org

@PKDana 11 жыл бұрын

Hm. Well this probably isn't helpful to you now, but I -think- you literally just take the ROW that the pivot point is in, rather than the column.

@michaelpostal 13 жыл бұрын

@hilaryeeee I Pay $4500 as an international student........ But it's not better than this............

@imorokr 13 жыл бұрын

I really think you're on to something...if our fucked up govt. ever decides to relieve the poor of their education (koch brothers have tried) a system like the one you have started would definitely even the playing field.