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\title{General Mathematics and CPS II}
\author{Exercise 7}
\date{February 26, 2014}
\maketitle

\begin{enumerate}

\item (Ivanov, p.\ 36, Problem~14.)  Show that
  \begin{enumerate}
  \item $R_{\ell_1} \, R_{\ell_2} = R_{\ell_2} \, R_{\ell_1}$ if and
  only if $\ell_1$ and $\ell_2$ are perpendicular;
  \item  $R_{\ell} \, H_A = H_A \, R_{\ell}$ if and
  only if $A \in \ell$.
  \end{enumerate}

\item Use the matrix form of the equation for a reflection (see
handout) to show that the composition of reflections about parallel
lines is a translation $\Pi_{\boldsymbol v}$.  Find an expression for the
translation vector $\boldsymbol v$.

\end{enumerate}


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