Suppose a linear transformation \(T:\RR ^2\rightarrow \RR ^2\) is such that
\[T\left (\begin{bmatrix}2\\-3\end{bmatrix}\right )=\begin{bmatrix}1\\0\end{bmatrix}\]
\[T\left (\begin{bmatrix}-1\\7\end{bmatrix}\right )=\begin{bmatrix}2\\1\end{bmatrix}\]
Then,
\[T\left (\begin{bmatrix}1\\4\end{bmatrix}\right )=\begin{bmatrix}\answer {3}\\\answer {1}\end{bmatrix}\]