Union of subspaces

Classic linear algebra exercise: the union of a subspace is a subspace if and only if one is contained in the other. This is also good practice with the definition of a subspace, and also shows how to prove statements of the form p implies (q or r)
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[@mohammedal-haddad2652]

Linear Algebra and Set Theory, that''s a very interesting combination. Thank you very much.

[@DivisionbyZer0]

excellent stuff, keep up the good work

[@peiwang3223]

Thank you soooo much, really enjoy your fantastic video, they really make my life easier.

[@dgrandlapinblanc]

Super clear. Thanks.

[@leonidasliao5288]

Really Cool THM, love it

[@AlvaroMiranda26]

Love your videos. Saludos desde Chile

[@drscott1]

Thanks!

[@Martin981202]

Could you please make a video of direct sums? Exams are coming and linear algebra is a tough one :) love your videos!

[@drpeyam]

Coming on Monday! But it’s already on the playlist

[@drpeyam]

Direct Sums ua-cam.com/video/GjbMddz0Qxs/v-deo.html

[@Martin981202]

Dr Peyam thank you!!

[@anamikasinha3030]

Can you tell me the way to find the union of two subsapces of a polynomial space of degree less than or equal to n.I request u to make a seperate video on polynomial space and their properties @dr_peyam

[@Shaan_Suri]

3:01 minecraft eating sounds

[@kirtiparashar1726]

Sir, considering the example that we have two sets w1 and w2, where w1 is {(0,1),(0,2),(0,3)} and w2 is {(1,0),(2,0),(3,0)} then if i want to find out the Union of these sets, will it be {(0,1),(0,2),(0,3),(1,0),(2,0),(3,0)} or the literal sum of the elements of w1 and w2 like (1,0)+(0,1) etc etc ? Please clear it sir.
If it is not the literal sum, then in the example given in the starting of the video, why we are like adding the two points and saying that it doesn't exist in the union, why even on the first hand we supposed it to exist in the union ?

[@danielaorozco9995]

I have the biggest crush on you 😍 thanks for the vids they’re gold!

[@newtonnewtonnewton1587]

Thanks D peyam السلام عليكم

[@coefficient1359]

@@8vabc338 I think it's some sort of a greeting. 🤷‍♀️😂🍳

[@user-vj7uc9tj7c]

@@8vabc338
I know a little Arabic, it says "Hello to you (Salam Alikum)"

[@newtonnewtonnewton1587]

@@8vabc338 D peyam is speaking several languages arabic.english.presian.french.and german i think

[@Handelsbilanzdefizit]

Haha..., "Subspace" reminds me on StarTrek :D
But seriously. A polynomial P(x)=ax³+bx²+cx+d is the dot-product of two vectors: (x³,x²,x,1)o(a,b,c,d)
So, the polynomial has a solution P(x)=0, when the Vectors are orthogonal. Because dot-product is zero.
Then (x³,x²,x,1) is element of the orthogonal subspace of (a,b,c,d). Or am I wrong?

[@drpeyam]

As the meme says: Well yes, but actually no! I agree, for fixed x, your x3 vector would be in orthogonal subspace, but in terms of polynomials, your dot product isn’t a dot product! A dot product has to spit out a number, not a polynomial