Suppose T : R2 R2 is a linear transformation. In each case, use the information provided

QUESTION:

Suppose \(T: \mathbb{R}^2 \rightarrow \mathbb{R}^2\) is a linear transformation. In each case, use the information provided to find the standard matrix A for T.

*a. \(T\left(\left[\begin{array}{l}1 \\ 0\end{array}\right]\right)=\left[\begin{array}{r}2 \\ -3\end{array}\right]\) and \(T\left(\left[\begin{array}{l}2 \\ 1\end{array}\right]\right)=\left[\begin{array}{r}-1 \\ 1\end{array}\right]\)

b. \(T\left(\left[\begin{array}{l}2 \\ 1\end{array}\right]\right)=\left[\begin{array}{l}5 \\ 3\end{array}\right]\) and \(T\left(\left[\begin{array}{l}0 \\ 1\end{array}\right]\right)=\left[\begin{array}{r}1 \\ -3\end{array}\right]\)

c. \(T\left(\left[\begin{array}{l}1 \\ 1\end{array}\right]\right)=\left[\begin{array}{l}3 \\ 3\end{array}\right]\) and \(T\left(\left[\begin{array}{r}1 \\ -1\end{array}\right]\right)=\left[\begin{array}{r}-1 \\ 1\end{array}\right]\)