Really basic linear algebra: subspaces of F[a,b]

[slugbunny]

Homework Statement

Determine which of the following sets of functions are subsets of F[a,b]

a) All functions f in F[a,b] for which f(a) = 0
b) All functions f in F[a,b] for which f(a) = 1

The Attempt at a Solution

Ok so I am just learning about vector subspaces. After reading the text multiple times, I am still at a lost. Can someone please explain to me in plain English what these evil math people want from me?

Thanks guys for your much appreciated help

 

[vela]

What's F[a,b] defined as? I assume it's some set of functions defined on the interval [a,b], but what particular properties must these functions have?

 

[slugbunny]

Thanks for your reply! Unfortunately F wasn't given any particular properties

 

[Hurkyl]

What is F[a,b] defined as?


P.S. did you mean "subset of F[a,b]" or did you mean "subspace of F[a,b]"?

 

[slugbunny]

oops sorry about that, I meant "subspace of F[a,b]"

F is the matrix with vectors a and b? :|

 

[Mark44]

F is the matrix with vectors a and b? :|

That doesn't make any sense. Instead of guessing, please tell us what F[a, b] means relative to this problem. It should say in the problem itself.

 

[vela]

OK, the first thing you need to do is go figure out what the notation "F[a,b]" means. Don't just make wild guesses. It should be explained in your textbook or notes somewhere.

 

[kaitamasaki]

You have to think about the basic closed under addition and closed under multiplication properties, to see if a) or b) satisfy them.
For example, would adding f(a)=0 and say g(a)=0 still be in this subspace?
What about for f(a)+g(a) = 1 + 1?
That should give you a clear hint.