###### Exercise 7

Suppose that \(T:\real^2\to\real^2\) is a matrix transformation and that

\begin{equation*}
T\left(\twovec{1}{1}\right) = \twovec{3}{-2}, \qquad
T\left(\twovec{-1}{1}\right) = \twovec{1}{2}\text{.}
\end{equation*}

Find the vector \(T\left(\twovec{1}{0}\right)\text{.}\)

Find the matrix \(A\) that defines \(T\text{.}\)

Find the vector \(T\left(\twovec{4}{-5}\right)\text{.}\)