linear algebra question

[JMaster]

I'm trying to study for a final in linear algebra that is next week, and I'm stuck on a problem.

Find a basis:
{P(t): p'(1)=p(2)} (p' is the derivative)
basically I know that this is subset of P3 (the space of all polynomials w/degree 3) is a subspace of P3 and I need to find the basis.

The answer in the book says that the basis is t, t^3 but I have no idea why. Can anyone help?

 

[Delusion2001]

check sparknotes.com

they have notes to help you with algebra. good luck

 

[Mister T]

is there an actual matrix here?
How are you sure its a subspace of P3?

Also, I don't have my linear algebra book handy, so do me a favor and look up
the exact definition of a basis and tell me.

It has been a solid 2 years since I took linear algebra.
I think I can help though.