Finding the Transition Matrix and [x]C for B and C Vectors

[Maxwhale]

Homework Statement

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

Homework Equations

The Attempt at a Solution

No clue :(

 

[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?