Answer
\begin{array}{l}
{\text { Step } 1 . \text { Apply the S mapping to }(M\ Q) \text { to get }(13\ 17) .} \\
{\text { Step } 2 . \text { Multiply result times } M :(13\ 17) \times\left[\begin{array}{cc}{3} & {5} \\
{2} & {3}\end{array}\right]} \\
{\qquad=(13 \times 3+17 \times 2\ \ \ \ \ 13 \times 5+17 \times 3)=(73 \ \ 116) \rightarrow(21\ \ 12)} \\ \\
{\text { Step } 3 . \text { Apply $S^{\prime}$ to $(21\ 12)$ to get $(U\ L)$} }
\end{array}
Work Step by Step
\begin{array}{l}
{\text { Step } 1 . \text { Apply the S mapping to }(M\ Q) \text { to get }(13\ 17) .} \\
{\text { Step } 2 . \text { Multiply result times } M :(13\ 17) \times\left[\begin{array}{cc}{3} & {5} \\
{2} & {3}\end{array}\right]} \\
{\qquad=(13 \times 3+17 \times 2\ \ \ \ \ 13 \times 5+17 \times 3)=(73 \ \ 116) \rightarrow(21\ \ 12)} \\ \\
{\text { Step } 3 . \text { Apply $S^{\prime}$ to $(21\ 12)$ to get $(U\ L)$} }
\end{array}
