##### Exercise1

Suppose that $$T:\real^3\to\real^2$$ and $$S:\real^2\to\real^2$$ are defined by the matrices $$A$$ and $$B$$ where

\begin{equation*} A = \left[\begin{array}{rrr} 3 \amp -1 \amp 0 \\ 1 \amp 2 \amp 2 \\ -1 \amp 3 \amp 2 \\ \end{array}\right], \qquad B = \left[\begin{array}{rr} 1 \amp -1 \amp 0 \\ 2 \amp 1 \amp 2 \\ \end{array}\right] \text{.} \end{equation*}
1. Evaluate the matrix transformation $$T\left(\threevec{1}{-3}{2}\right)\text{.}$$

2. Evaluate the matrix transformation $$S\left(\twovec{-2}{2}\right)\text{.}$$

3. Evaluate the matrix transformation $$S\circ T\left(\threevec{1}{-3}{2}\right)\text{.}$$

4. Find the matrix $$C$$ that defines the matrix transformation $$S\circ T\text{.}$$

in-context