# Math Help - Linear Spaces

1. ## Linear Spaces

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

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

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.

$q(t) = a+bt+ct^{2}$
$\ss =(1,t,t^2)$

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

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

Thanks.

2. You're on the right track. Your derivative should be b+2ct, not t+2ct. Evaluating q' and q at 1 and 2 respectively, you get b+2c = a+2b+4c. This is a linear system of three unknowns and one equation, so it's just basic linear algebra from here.

3. Thanks, got it!