Finding transition matrix

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 :(

gabbagabbahey

Well, if you call your transition matrix [itex]T[/itex], then

[tex]\begin{pmatrix} 1 \\ -3 \end{pmatrix}= T \begin{pmatrix} 3 \\ 1 \end{pmatrix}[/tex]

and

[tex]\begin{pmatrix} 5 \\ 0 \end{pmatrix}=T \begin{pmatrix} -1 \\ -2 \end{pmatrix}[/tex]

[tex]\Rightarrow \begin{pmatrix} 1 & 5 \\ -3 & 0 \end{pmatrix}= T \begin{pmatrix} 3 & -1 \\ 1 & -2 \end{pmatrix}[/tex]

...is that enough to get you started?