SUBSPACES - LINEAR ALGEBRA

[@TheMrMefistofele]

This theory is very useful and well explained, but I think you should show more solved exercises. Or show how to solve different problems.

[@arshiya8910]

My mathematics professor doesn't explain things well.... really helpful 👍

[@fan_dan_go1545]

The way R^2 is not a subspace of R^3 makes sense to me is that you could have a plane in R^3 that does not passes through the origin ( meaning it does not contain the zero vector) from looking at the sketch @ 11:40

[@zoranivanic3543]

Even the plane (in R^3) passing through the origin would not be a subspace because it has a value for Z coordinate meanwhile in R^2 there is no such thing. R^2 isn't just R^3 with Z set to zero. Z doesn't exist in R^2. This is why the statement is false.

[@benzeltser9851]

Hard subject, well explained many of us will not get it the first or second time, give it another Chance.

[@kvotheosem-sangue]

Thanks for the astounding class, keep at it!

[@anadiru4382]

Amazing! Finally i understood the subspaces of the vector spaces

[@saulorocha3755]

Congratulations, you managed to make me understand vector space a little bit LOL.

[@KevaneeFagan]

To be exact, what makes you know that the vector is in the span? what do I have to identify to let me know that? Am I to go over span of vectors first?

[@nv3796]

Last Q really makes it clear

[@ThisWasEpicness]

you dont explain much about the why, you do but like not enough to understand :( like 4:30 "we know its in the subspace because it is in the span... like how is it in the span why waaaaaa

[@YvngAnakin]

Lol are you studying for diffyq exam tomorrow?

[@ziliestarrive]

Because a span of some vectors is just a linear combination of those vectors, meaning any way you add those vectors together after multiplying them by any real number scalar. Basically span(v1,v2...vn) = a1*v1+a2*v2...+an*vn. You can have any vector and any number of them you want. In that particular case, you got v1 = [-1,1,1], v2=[0,-6,2], v3=[1,0,0], and the scalars a,b,c, which can basically be anything and you add the vectors together after multiplying by the scalars. Therefore, you got a span of v1,v2,v3, which is same as span([-1,1,1], [0,-6,2], [1,0,0]). Since his previous proof in this video showed that span of any number of vectors is a subspace of the vector space that they belong to, that particular form of vector is a subspace to the vector space of column space size 3. Correct me if I'm wrong.

[@YcJuice5]

This is really nice and understandable 😊❤

[@linahajji560]

thank youuu so much for the explanation

[@sarkersaadahmed]

9:29 hoiw can you exactly proov that the span theorm is correct?

[@nguyenhoang4410]

Thank you, sir!

[@danianaj4883]

This was really helpful!!!

[@schang_lh]

Sorry, but is there any word definition of subspace? Like what is it and what is it used for? Because I understand how to do the math but when asked to explain what it is, I would have no idea what to say. If anyone knows, plz let me know. >< Thanks!

[@georghieronymus9935]

This topic is getting into advanced mathematics. Layman's explanations are harder to come up with. You need to understand the notion of sets, vectors, vector spaces to draw conclusions about those mathematical objects and topics, and how they work together. I don't think this is for average people to understand, it's for people who are talented in mathematics. If you need to pass a course in college as part of your degree, zoom in on it and learn how to solve the problems mechanically and ignore context and meta.

[@hasaniqbal233]

@@georghieronymus9935 r/iamverysmart

[@ziliestarrive]

@@georghieronymus9935 Instead of writing all that you could have just either said it's not useful for laymen and you won't explain it, or just attempt to explain it.

[@li_bbywilkinson]

L

[@zamokuhleduma3673]

Thank you so much

[@christiancardenas1988]

Great stuff

[@Seven_Pictures_HK]

From 12:10 onwards, you said R3 has to give that vector to R2 and therefore R2 is a subset of R3 which sounds similar to the time you drew the diagram at 11:39. That I don't understand.

[@Trevtutor]

R2 is not a subset of R3. We are working with a subset of R3, but R2 is not that subset.

[@AshleySurajHermon]

very good and helpful

[@alankuo2727]

fantastic vid

[@suprememaster1951]

Every subspace of R5 that contains a nonzero vector must contain a line. Is this statement true?

[@JZX619]

Really helpful!

[@KevaneeFagan]

I don't find your explanations to be entirely clear. You're just saying things and writing things down but not saying why. Your explanations are too shallow man.You're losing me on the second example.

[@wirito]

mmmm they are actually extremely clear....

[@ThisWasEpicness]

ahlie they are not clear at all

[@hasaniqbal233]

@@ThisWasEpicness found the toronto mans

[@sisarka468]

You should try going to my professor's lecture, you wouldn't understand a god damn thing. This explanation is so much better

[@noahjohnson2601]

In order to be a subspace of a vector does the subspace and vector have to have the same dimensions?

[@maryammozayan9015]

yes

[@li_bbywilkinson]

Okay you slayed

[@lemyul]

thanks tre

[@AfzalKhan-rw5bh]

Thank you sir

[@eruditionchn1176]

Awesome

[@amirhamza246]

Why aren't you my professor

[@josephtuohey1606]

I am still confused TheTrevTutor

[@swaroop_765]

nice

[@issacoh4775]

Is R^3 a subspace of R^2?

[@aidyn9394]

aituwniki tut?

[@statube9982]

It is a nice tutor even a university professor doesn't explain like this. But I have some doubt on one of the last three questions, which is question number 3. I think the answer should be TRUE but you said FALSE. Why I said TRUE is, a vector in R2 means that the third axis, which is axis Z is 0 and it is omitted. Therefore, R2 is a subspace of R3. If you or anyone who reading this can explain that my argument is wrong or right. Thank you.

[@PeterBouSaada]

still feels like im trying to read turkish

[@PeterBouSaada]

im hopeless at this point lmao

[@siyabongazungu1640]

your vector is wrong

[@omerfeyyazselcuk7325]

**we can generalize it more**

[@ziadtorsson922]

Wasted my time....stop the proofs give some exercises

[@nigerianscammer4640]

you must be a highschool student

[@ziadtorsson922]

@@nigerianscammer4640 no im a master degree student in civil engineering you piece of shit

[@hassankone6175]

Ziad Torsson chill

[@nigerianscammer4640]

@@ziadtorsson922 proving is 50% of a mathematics subject. If you're not being taught that, you're being stripped of valuable information

[@larsveldhuis8820]

@@ziadtorsson922 pop a xanny bro

[@Paul-ry3jq]

whos tryna get the pipe?

[@MuhammadAyaz-mt6hw]

aoooncha boolna yra

[@theleonidaspartan]

V1 zulul

[@Ckjohn77kg]

My teacher owes you a paycheck

[@الفشيخالفشيخ-و5ص]

what a cancerous subject

[@dynamo-_-5962]

بشر شو صارلك

[@noahjohnson2601]

In order to be a subspace of a vector does the subspace and vector have to have the same dimensions?

[@gauravnagamaheswarpattem7069]

I think yeah!! what I thought was:- from the last example, it is looking obvious that the subspace and the vector have to possess the same dimensions...