
Basis Matrix
I was tutoring yesterday and I got caught completely offguard by this question:
Let $\displaystyle B= \{ 1+t^2,3t+4t^2,1+2t4t^2 \} $
Find $\displaystyle [13t+5t^2]_B $ and find q such that [tex]q_B = (1,3,2)
I forgot most of my linear algebra, and I don't have my notes with me, would anyone please explain this to me? Thanks.

You want, $\displaystyle 1  3t + 5t^2 = a\left( {1 + t^2 } \right) + b\left( {3  t + 4t^2 } \right) + c\left( {1 + 2t  4t^2 } \right)$.
So
$\displaystyle \begin{gathered}
a + 3b + c = 1 \hfill \\
 b + 2c =  3 \hfill \\
a + 4b  4c = 5 \hfill \\
\end{gathered}
$
SOLVE!