What is the Dimension and Linear Independence of Subspaces?

[seang]

I'm having trouble understanding bases outside of R^n; I've got a handle on those I think.

Here are some examples:

13. In C(-Pi,Pi), find the dimension of the subspace spanned by 1, cos(2x), and cos^2(x).

14. Find the dimension of the subspace of P3 spanned by x, x-1 , x^2+1, x^2-1

I really don't know how to begin either of these

Thanks for any input.

 

[radou]

Begin with the definition of a span: http://mathworld.wolfram.com/VectorSpaceSpan.html" .

 

[seang]

hmm I already know about spans but that might have helped actually. thanks.

 

[HallsofIvy]

More important, I think, is the definition of "linearly independent". How many of those given functions are linearly independent?