# Thread: Basis Matrix

1. ## Basis Matrix

I was tutoring yesterday and I got caught completely offguard by this question:

Let $B= \{ 1+t^2,3-t+4t^2,-1+2t-4t^2 \}$

Find $[1-3t+5t^2]_B$ 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.

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

SOLVE!