Exercise7

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

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

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

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