4.9.1: Coordinatization.
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Given the ordered basis
$$ \mathcal{B} = \left\{ A_1 = \begin{bmatrix} 0 & -5 \\ -8 & -6 \end{bmatrix}, A_2 = \begin{bmatrix} 8 & 0 \\ -9 & 2 \end{bmatrix}, A_3 = \begin{bmatrix} 9 & 6 \\ -6 & -5 \end{bmatrix}, A_4 = \begin{bmatrix} -9 & 2 \\ 9 & 8 \end{bmatrix} \right\} $$
find $[A]_{\mathcal{B}}$, the coordinates of $A = \begin{bmatrix} 20 & 0 \\ -15 & -33 \end{bmatrix}$ with respect to $\mathcal{B}$.
$[v]_{\mathcal{B}} = \begin{bmatrix} \\ \\ \\ \end{bmatrix}$