# Determine if the following is a vector space

• Feb 26th 2010, 11:29 PM
chickeneaterguy
Determine if the following is a vector space
Hello everyone. I'm new here. I have a practice test that I'm working on for my linear algebra class and I sorta get the gist of determining whether or not something is a subspace or not but I'm having trouble with this one:

I did terrible in Calc 2 so the whole derivative thing isn't too familiar to me.

http://www.mathhelpforum.com/math-he...1&d=1267259282
• Feb 26th 2010, 11:33 PM
Drexel28
Quote:

Originally Posted by chickeneaterguy
Hello everyone. I'm new here. I have a practice test that I'm working on for my linear algebra class and I sorta get the gist of determining whether or not something is a subspace or not but I'm having trouble with this one:

I did terrible in Calc 2 so the whole derivative thing isn't too familiar to me.

http://www.mathhelpforum.com/math-he...1&d=1267259282

I also have some T/F questions on it. I have guesses but nothing I know for a fact.

True/False?:
1. P2 is a Subspace of P3 (I think it's true)
2. D[0,1], the set of all differential functions over [0,1] is a subspace of C[0,1] (I think it's true)
3. {ax^2 + bx + c : b = 0} is a subspace of P2 (I think it's true....or maybe not)

Obvious things...look for them. $\displaystyle (f+g)'(2)=f'(2)+g'(2)=0+0=0$. $\displaystyle \left(\alpha f\right)(2)=\alpha f'(2)=\alpha \cdot 0=0$. etc.
• Feb 26th 2010, 11:34 PM
chickeneaterguy
Quote:

Originally Posted by Drexel28
Obvious things...look for them. $\displaystyle (f+g)'(2)=f'(2)+g'(2)=0+0=0$. $\displaystyle \left(\alpha f\right)(2)=\alpha f'(2)=\alpha \cdot 0=0$. etc.

So I don't even need to bother with derivatives or anything?

EDIT: nvm...I realized how obvious it is. Gosh...that's ridiculously easy.
• Feb 27th 2010, 04:34 AM
xalk
Quote:

Originally Posted by chickeneaterguy

So I don't even need to bother with derivatives or anything?

EDIT: nvm...I realized how obvious it is. Gosh...that's ridiculously easy.

How would you prove :

for all ,f,gεV ..........f+g=g+f ??
• Feb 27th 2010, 06:12 AM
HallsofIvy
As you would prove any such fundamental statement- from the definition:

f+ g is defined as the function such that (f+g)(x)= f(x)+ g(x).
Similarly, g+ f is defined as the function such that (g+f)(x)= g(x)+ f(x).

Saying that f+ g= g+ f is just saying that, for all x, f(x)+ g(x)= g(x)+ f(x) - and that's true because f(x) and g(x) are numbers and addition of numbers is commutative.