Applying Definition MR,
\begin{align*}
\vectrep{C}{\lt{T}{2-5x+x^2}}&=\vectrep{C}{\colvector{-2\\-4}}
=\vectrep{C}{2\colvector{3\\4}+(-4)\colvector{2\\3}}=\colvector{2\\-4}\\
\vectrep{C}{\lt{T}{1+x-x^2}}&=\vectrep{C}{\colvector{1\\-5}}
=\vectrep{C}{13\colvector{3\\4}+(-19)\colvector{2\\3}}=\colvector{13\\-19}\\
\vectrep{C}{\lt{T}{x^2}}&=\vectrep{C}{\colvector{1\\9}}
=\vectrep{C}{(-15)\colvector{3\\4}+23\colvector{2\\3}}=\colvector{-15\\23}
\end{align*}
So the resulting matrix representation is
\begin{align*}
\matrixrep{T}{B}{C}
&=
\begin{bmatrix}
2 & 13 & -15 \\
-4 & -19 & 23
\end{bmatrix}
\end{align*}