Let b_{1} = \left [ \begin{matrix} 1 \\ -3 \end{matrix} \right ] , b_{2} = \left [ \begin{matrix} -2 \\ 4 \end{matrix} \right ] , c_{1} = \left [ \begin{matrix} -7 \\ 9 \end{matrix} \right ] , c_{2} = \left [ \begin{matrix} -5 \\ 7 \end{matrix} \right ] and consider the bases for \mathbb{R} ^{2} given by \mathcal{B} = \{b_{1},b_{2}\} and \mathcal{C} = \{c_{1},c_{2}\} .
a. Find the change-of-coordinates matrix from \mathcal{C} to \mathcal{B} .
b. Find the change-of-coordinates matrix from \mathcal{B} to \mathcal{C} .