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 \(S\circ T\text{.}\)

in-context