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

slugbunny

1. The problem statement, all variables and given/known data

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


3. 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

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.