Linear Combinations and Span

[AntoMelta]

Good, I like that you share this video Understanding linear combinations and spans of vectors, I wish success always

[willamricard]

Nice Video Understanding linear combinations and spans of vectors That You Share , So Very Nice Thanks You

[imegatrone]

I Really Like The Video Understanding linear combinations and spans of vectors From Your

[bundawartini]

Your Video Understanding linear combinations and spans of vectors Is Very Useful Sharing

[LostAngel01234]

What about in R3 (3 Space) how can you tell if they span R3 or not??

[fliskmayhem]

@LostAngel01234 First of all, you'll need at least 3 diffrent vectors (call them v_1, v_2 and v_3). Each with dimension 3, so they'll look like (x,y,z). Second, it must be impossible to write one of these vectors as a linear combination of the other 2 vectors. I.e. : c_1 v_1 + c_2 v_2 + c_3 v_3 = (0,0,0) only if c_1 = c_2 = c_3 = 0, the three vectors span R3. If there's another solution for the c_i's, it means the vectors span up a plane or a straight line in R3, but not whole R3.

[Byron10301]

2:02 ... ummmm Sal, what did you just draw?!!! LOL hahaha

[bloodyjack111]

@khanacademy how do you write so neatly with your mouse

[Byron10301]

@bloodyjack111 He uses a bamboo writing tablet. It's a neat device, I have one too. 

[Earphony]

OOOOOOOOOOOOOOOOOOOOOOOOOOO now i get it.

Thx Sal.

[SochoChun]

sweet... it's much better than my professor's lessons, this is a really good revision lesson before my test

[waseem1173]

Now thats a real teacher. man i love you . you're a life saver

[Dinonu]

who the fuck hits the dislike button on this?

[mufc4everch]

@Dinonu prbly accidents

[PhilChern]

what's the program that he uses for this video?

[15071985gucar]

in the moment 04:13:, what if you don´t ignore the vector C, it seems like the three are linearly independent, I mean you got three vectors linearly independent in a bidimensional space, if the vectors were coeficients of a linear sistem of equations, that sistem would be indeterminated but compatible, ¿ how you interpretate that situation?

[Hockeysktr17]

You're a Bauss.

[acc771]

you are truly effecting peoples lives - giving them the ability to do things they never would have been able to and we can never thank you enough. you have a gift and you have one of the best hearts the world has ever known

[acc771]

you are truly effecting peoples lives - giving them the ability to do things they never would have been able to and we can never thank you enough. you have a gift and you have one of the best hearts the world has ever known

[Edwrath]

My University Day:

-Sleep through morning lectures.

-Watch khanacademy versions of my lectures

-Play guitar all afternoon

[visiting31]

@Edwrath: hear! hear!

[KanzakiGNT]

@Edwrath + Add some MIT lectures by G. Strang :D

[omgthatscrazyx]

everything you are doing is perfect. you are the ideal human being

[tehmadcap]

Sal you are the best! <3

[oluwatoba11]

I think I need to take some moment of pause sometimes in the exams too! Great guy!!!

[publicanimal]

You are a god. with the graphical representation of vector space R2 I finally understood the concept of linear combos. thanks

[shaneymane15]

My textbook is so f**king vague and complex. Idk what I would do without the interwebs.

[Benjikj]

Dear Khan Academy, can you please not make any more videos that are as long as this!!! I don't wanna watch a 20 minute video, feels too much like a lecture! Please more bitesize chunks!! ;) thnaks keep up the good work

[lexmarklogi]

who the hell down voted this?

[munchmich]

nice one mate. that helped alot 

[MrWhoabuddy]

at 17:55, you forgot to write the 2 next to your x-sub1 when you divided the right side by 3.

[stoudc]

I would just like to say that this is more helpful than any lecture I have taken. What khanacademy has covered in 10 minutes is more than we covered in the first 3 weeks of class and makes sense perfectly!

[teranteran1]

The one dislike came from a guy who found this Video a minute before his exam.

[matildakamberi]

thank you so much for this video

[haro123ish]

love you man, i always wondering what a span was. my teachers have failed to explain this so far. thank you

[Feroyn]

I passed Linear Algebra because of these videos. You're the best, Khan!

[TheTheEmpty]

@Feroyn totally agree!

[narical]

we can never get rid of retards from this world!!.....the 1 dislike proves it!!!

[fatgingerANGRY]

Thanks for getting me though 8th grade.

[squarepusher303]

awesomeness!

[isoman2kx]

Thanks for the help Sal! You should reply to some comments though every once in a while though :)

[n1a1s1i1m]

Chuck Norris once taught a kid math. He is now Sal.

[AcutePorphyria]

@n1a1s1i1m A Chuck Norris joke. Wow.

[pardavillc]

You totally rock dude!

[scientist071]

Thanks!

[rockythapa]

All the Linear combination of vector are Linear combiantionn lol 

[ksb916]

Thx this really helps :)

[EwoudCP]

Wow. This is really useful. I've been trying to make sense of the idea of the span, but I tend to see things other people don't. More frustratingly, I tend to not see things that other people do. Thanks for the video. I'll definitely keep your playlists in my bookmarks.

[bryannamelenhorst]

thank the lord i found these video's. you are an amazing teacher!

[salmandanny]

you provide us awesome lecture which helps us in getting our foundation strong ...

[disornr]

God bless you!!

[napatnutnut]

you make me more understand (: THX

[talha6k]

You are great! God bless....

[adhiliqbal]

dear khan is it possible to merge all theses linear algebra videos together, so that we can download them to our ipods

[EZ1331]

@adhiliqbal ya i agree!

[Ace12174]

This is definitely helping me understand span. It's starting to sink in! lol Thanks! There's one question I have though, why do you multiply (at 17:24) when finding any C1 and C2 by -2? thanks =) (Grade 12 Calculus and Vectors)

[GMmarine]

@Ace12174 He multiplied by -2 so he could find one variable at a time - which in this case wasC2 - so after he found the value of C2 he could find the value of C1. Its called solving a system of linear equations by using elimination.

[Ace12174]

@GMmarine Oh, thanks, I was better at substitution compared to elimination so that's probably why I didn't understand

[flamingmonkey923]

Why don't you teach my math 220 class? Why?

[hifhif123]

19:09 you can sense the suspicion in your voice right about there, when c2 was equal to zero

[dsprack]

Dear Khan Academy, you are amazing.

[PCDK]

haha... he draws a penis!

[aszianslovehate3051]

ahh....thank you so much :) i found this..before my exam which is tom :) thnx

[thomapple]

Hey, I've got a question for you: at the very beginning, you write:

v1, v2, ..., vn in R^n

But does that mean you have to choose the same numbers of vectors as the number of dimensions you're working in (n in this case)? (uh sorry for my English, I hope this is clear)

Wouldn't it be better to write for instance:

v1, v2, ... , vi in R^n ?

[Ben1220]

You're absolutely right, it doesn't matter how many vectors you have, linear combinations are defined for any set of vectors. He probably should have chosen a different name for the first n, but this doesn't matter if you realise that the two n's are different. Well done for spotting that :P

[hai2410]

@Ben1220 and @thomapple

I think he's right actually. R^n is n-tuples of real numbers. If you're working in R^2, you have two dimensions to work in and so you get [x1,x2], R^3 [x1,x2,x3], so it follows from that.

[azfanification]

you rock my khan!!

[sherajr]

I'm so glad I found this before my midterm!!

[kamyarghofrani]

what is your name?

[Smilinggoose]

I found this really useful. Thanks a lot!

[yuropod]

"So I had to take a moment of pause..."

I love this guy

[brco2003]

Never mind; you fixed it. (I knew you could never make a mistake.)

[brco2003]

Sal, at 18:00, the x1 term is missing its factor of 2.

[EXIY900]

Great videos, more Linear Algebra :)

[joeyjoey1122]

Thanks soo much, Im taking LINEAR ALGEBRA now!

[Argonaut1337]

Yes, more on Linear Algebra!!!!

[GoldAK47]

OMGGGGG... i had a lecture about this this morning, did not understand it and I log in YouTube to find out you uploaded a vid regarding this subject.

Thanks man