- #1
lockedup
- 70
- 0
1. Homework Statement :
Prove: A set U [tex]\subset[/tex] V = (V, [tex]\oplus[/tex], [tex]\odot[/tex]) is a vector subspace of V if and only if ([tex]\forall[/tex]u1, u2 [tex]\in[/tex] U) (1/2 [tex]\odot[/tex] (u1 [tex]\oplus[/tex] u2) [tex]\in[/tex] U) and ([tex]\forall[/tex]u [tex]\in[/tex] U) ([tex]\forall[/tex]t [tex]\in \mathbb{R}[/tex]) (t [tex]\odot[/tex] u [tex]\in[/tex] U).
3. The Attempt at a Solution :
I don't have the first clue. To me, it seems that there is missing information. I know that for a subspace, it is sufficient to prove only closure under addition and scalar multiplication. Maybe he's defining a different sort of addition? Ugh, the whole proof thing is actually pretty new to me. I only started doing simple proofs last semester in Discrete Mathematics...
Prove: A set U [tex]\subset[/tex] V = (V, [tex]\oplus[/tex], [tex]\odot[/tex]) is a vector subspace of V if and only if ([tex]\forall[/tex]u1, u2 [tex]\in[/tex] U) (1/2 [tex]\odot[/tex] (u1 [tex]\oplus[/tex] u2) [tex]\in[/tex] U) and ([tex]\forall[/tex]u [tex]\in[/tex] U) ([tex]\forall[/tex]t [tex]\in \mathbb{R}[/tex]) (t [tex]\odot[/tex] u [tex]\in[/tex] U).
3. The Attempt at a Solution :
I don't have the first clue. To me, it seems that there is missing information. I know that for a subspace, it is sufficient to prove only closure under addition and scalar multiplication. Maybe he's defining a different sort of addition? Ugh, the whole proof thing is actually pretty new to me. I only started doing simple proofs last semester in Discrete Mathematics...
Last edited: