[M] in Exercises, find the -matrix for the transforma-tion

QUESTION:

[M] In Exercises 30 and 31, find the \(\mathcal{B} \text {-matrix }\) for the transformation \(\mathbf{x} \mapsto A \mathbf{x}\) when \(\mathcal{B}=\left\{\mathbf{b}_{1}, \mathbf{b}_{2}, \mathbf{b}_{3}\right\}\).

\(A=\left[\begin{array}{rrr}-14 & 4 & -14 \\ -33 & 9 & -31 \\ 11 & -4 & 11\end{array}\right], \mathbf{b}_{1}=\left[\begin{array}{r}-1 \\ -2 \\ 1\end{array}\right], \mathbf{b}_{2}=\left[\begin{array}{r}-1 \\ -1 \\ 1\end{array}\right], \mathbf{b}_{3}=\left[\begin{array}{r}-1 \\ -2 \\ 0\end{array}\right]\)