Having a hard time understand subspaces, someone guide me here please

S = { x1, x2 ,x3 } ER| x1 + x2 = 2x3 is this subset a subspace? Thanks, ill donate 3fg if you can give me help in the next 15 mins.

is the ER supposed to be belongs to the set of reals?

yes

pretty sure this does since it's a plane. Idk, haven't touched this stuff in a while. I'll read some stuff and get back to ya

Edit: yeah, since it's a plane, the sum of any vectors in the set is also in the set. Therefore, it is a subspace (does that definition sound familiar to you?)

This post was edited by zackill4 on Sep 20 2013 02:21am

ok merci. just pm me if you get anywhere

Here's my attempt at a proof

let v and w be any two vectors in the set

then since x1+x2-2x3 = 0, v * [1 2 -2] = 0 and w * [1 2 -2] = 0

(v+w) * [1 2 -2] = v * [1 2 -2] + w * [1 2 -2] = 0, so v+w is also in the set


Also contains origin and works for all scalars, yadda yadda

This post was edited by zackill4 on Sep 20 2013 02:33am

I think you have to verify the 10 axioms to show it's a subspace. It's been a while since I took Linear Algebra, so I'm not certain.

ya

pretty much