Find a basis of the linear space and thus determine the dimension.

$\displaystyle q(t) : q'(1)=q(2)$

Where q is a subset of Q_2: all polynomials of degree less than or equal to 2. I had to change it from p to q so the forum didn't make it a smiley...

I'm not sure what to do here. I created an arbitrary form of q(t) and q'(t) and found a basis for each of these.

$\displaystyle q(t) = a+bt+ct^{2}$

$\displaystyle \ss =(1,t,t^2)$

$\displaystyle q'(t) = t+2ct$

$\displaystyle \ss = (t)$

Now I'm lost, and I'm pretty certain I was never on the right track. Any help would be extremely appreciated.

Thanks.