Answer
\begin{array}{l}
{\text { Step } 1 . \text { Apply the S mapping to }(U\ L) \text { to get }(21\ 12) .} \\
{\text { Step } 2 . \text { Multiply result times } M^{\prime} :(21\ 12) \times\left[\begin{array}{cc}{23} & {5} \\
{2} & {23}\end{array}\right]} \\
{\qquad=(21 \times 23 +12 \times 2\ \ \ \ \ 21 \times 12+23 \times 3)=(507 \ \ 381) \rightarrow(13\ \ 17)} \\ \\
{\text { Step } 3 . \text { Apply $S^{\prime}$ to $(13\ 17)$ to get $(M\ Q)$} }
\end{array}
Work Step by Step
\begin{array}{l}
{\text { Step } 1 . \text { Apply the S mapping to }(U\ L) \text { to get }(21\ 12) .} \\
{\text { Step } 2 . \text { Multiply result times } M^{\prime} :(21\ 12) \times\left[\begin{array}{cc}{23} & {5} \\
{2} & {23}\end{array}\right]} \\
{\qquad=(21 \times 23 +12 \times 2\ \ \ \ \ 21 \times 12+23 \times 3)=(507 \ \ 381) \rightarrow(13\ \ 17)} \\ \\
{\text { Step } 3 . \text { Apply $S^{\prime}$ to $(13\ 17)$ to get $(M\ Q)$} }
\end{array}
