# subspaces

• Feb 21st 2011, 04:41 PM
rabih2011
subspaces
determine whether w={f:f(x)greater than or equal to 0} is a subspace of C, the set is continuous functions on the real numbers
• Feb 21st 2011, 04:58 PM
DrSteve
If f is in w, think about the function -f.
• Feb 21st 2011, 07:57 PM
Raoh
In other words,is $w$ closed under scalar multiplication ?
• Feb 21st 2011, 10:05 PM
FernandoRevilla
Quote:

Originally Posted by Raoh
In other words,is $w$ closed under scalar multiplication ?

No, it isn't. Look at DrSteve's post. For example choose $f(x)=1$ for all $x\in \mathbb{R}$ then, $f\in W$ however $[(-1)f](x)=(-1)f(x)=(-1)\cdot 1=-1$ . That is, $(-1)f\not\in W$ .

Fernando Revilla
• Feb 22nd 2011, 02:35 AM
Ackbeet
Quote:

Originally Posted by FernandoRevilla
No, it isn't. Look at DrSteve's post. For example choose $f(x)=1$ for all $x\in \mathbb{R}$ then, $f\in W$ however $[(-1)f](x)=(-1)f(x)=(-1)\cdot 1=-1$ . That is, $(-1)f\not\in W$ .

Fernando Revilla

Just my hunch, but I think Raoh understands the problem, and is trying to get the OP'er to ask the question in post #3. Could be off on that, though.
• Feb 22nd 2011, 10:43 AM
Raoh
My question was meant to help the OP'er.
• Feb 22nd 2011, 11:30 AM
FernandoRevilla
Quote:

Originally Posted by Raoh
My question was meant to help the OP'er.

Sorry, by error I thought your post was from the original poster. :)

Fernando Revilla
• Feb 22nd 2011, 01:38 PM
DrSteve
Wow - it's not too hard to get thanked around here - very polite group!