Hey, this is for a intro to linear algebra class.

Find a basis for those that are subspaces. From P2 to P2.

{p(t): p'(1) = p(2)} (p' is the derivative)

The answer is that it is a subspace with a basis 1-t, 2-t^2 (t squared)

I just can't seem figure out how to get to this conclusion. Any help would be greatly appreciated.