(1 point) Let $T: \mathbb{R}^3 \to \mathbb{R}^2$ be a linear transformation such that
$T\begin{pmatrix} 1 \ 0 \ 0 \end{pmatrix} = \begin{pmatrix} -1 \ 2 \end{pmatrix}$, $T\begin{pmatrix} 1 \ 1 \ 0 \end{pmatrix} = \begin{pmatrix} 1 \ -1 \end{pmatrix}$, $T\begin{pmatrix} -1 \ 2 \ 1 \end{pmatrix} = \begin{pmatrix} -2 \ 3 \end{pmatrix}$.
Find the following:
$T\begin{pmatrix} 1 \ 0 \ -1 \end{pmatrix} = \begin{pmatrix} \\
\end{pmatrix}$
Hint: First write $\begin{pmatrix} 1 \ 0 \ -1 \end{pmatrix}$ as a linear combination of $\begin{pmatrix} 1 \ 0 \ 0 \end{pmatrix}$, $\begin{pmatrix} 1 \ 1 \ 0 \end{pmatrix}$, and $\begin{pmatrix} -1 \ 2 \ 1 \end{pmatrix}$.
