Thread: Subspaces.

Hey again!
Sorry, I don't mean to fill up the entire forum, but as I said in my other post, I have an exam and I need all the help I can get. I figured if anyone can answer these for me while I study, bonus! Here's a few questions I could use the answers for.


I put them as pictures because they're much more clear that way than if I tried to type them.

Again, thank you to whoever is willing to help!

For 1:

.

So we have .

.

.

For 2 :

(i)



Next step?

(ii)



Next step?

two more hints:

if <x,u> = 0, and <x,v> = 0 then certainly <x,u+v> = 0.

now can we say that if u is in U, and v is in V, that u,v are in U+V?