Prove W = {(a, b) | a = -b} is a Subspace of R^2

[@johnsecen5552]

Are there any examples for this in finite fields?

[@Americabeatz]

you are such a good teacher! i just cant understand why a subset being non empty is the same as 0 being in the subset.

[@shktlaiamxt717]

0 is an element, therefore the set is non-empty.

[@Ashutosh-f1p]

Only 0 belong to real no s.t
a=-a

[@afj810]

​Why is 0 chosen to demonstrate this? I never see any other element used to show that the set is non-empty.​@@shktlaiamxt717

[@VikSun14618]

Thank you for doing so many examples. I think I understand it now.

[@TheMathSorcerer]

great!

[@geniusmathematics9123]

Hats off sir..

[@cosovobas]

You're Awsome Teacher! , I can now understand better vectorial subspace , Thank You.

[@TheMathSorcerer]

Awesome!

[@GEhehloopf]

In your previous examples you plugged in an arbitrary number to prove that it's wrong. I plugged in X = (5, 6) Y = (1, 2)
and then did the vector addition but it proves it wrong. Could you please clarify this regarding closed vector addition?

[@user-nk6jt7qi8p]

because x and y need both to belong to subspace of W so the first element of the vectors has to be the opposite of the second element which isnt the case of your vectors

[@josecarlos-zc9hy]

Hi teacher! Help, please...Prove that the set of vectors B={(a,1,1)} is a vector subspace?

[@veereshg6600]

super🔥

[@muhammadsufyan6457]

what if b=2a+1

[@shqdowfb9444]

Wt abou' negatve alpha????

[@geniusmathematics9123]

Then also the condition holds good

[@elmokillah123]

ong hi

[@aryansudan2239]

ez