##### Exercise1

Suppose that $$T$$ is the matrix transformation defined by the matrix $$A$$ and $$S$$ is the matrix transformation defined by $$B$$ 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}{rrr} 1 \amp -1 \amp 0 \\ 2 \amp 1 \amp 2 \\ \end{array}\right] \text{.} \end{equation*}
1. If $$T:\real^n\to\real^m\text{,}$$ what are the values of $$m$$ and $$n\text{?}$$ What values of $$m$$ and $$n$$ are appropriate for the transformation $$S\text{?}$$

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

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

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

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

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