Finding transition matrix

1. Nov 9, 2008

Maxwhale

1. The problem statement, all variables and given/known data

Find the transition matrix from B to C and find [x]C

B = {(3,1), (-1,-2)}
C = {(1,-3),(5,0)}

[x]B = [-1 -2]T

2. Relevant equations

3. The attempt at a solution
No clue :(

2. Nov 9, 2008

gabbagabbahey

Well, if you call your transition matrix $T$, then

$$\begin{pmatrix} 1 \\ -3 \end{pmatrix}= T \begin{pmatrix} 3 \\ 1 \end{pmatrix}$$

and

$$\begin{pmatrix} 5 \\ 0 \end{pmatrix}=T \begin{pmatrix} -1 \\ -2 \end{pmatrix}$$

$$\Rightarrow \begin{pmatrix} 1 & 5 \\ -3 & 0 \end{pmatrix}= T \begin{pmatrix} 3 & -1 \\ 1 & -2 \end{pmatrix}$$

...is that enough to get you started?