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\begin{document}

\title{General Mathematics and ACM II}
\author{Exercise 20}
\date{May 11, 2011}
\maketitle

\def\e{\mathrm{e}}
\def\i{\mathrm{i}}
\def\d{\mathrm{d}}

\begin{enumerate}

\item Without using a computer, compute the discrete Fourier transform
of the vector
\[
  v =
  \begin{pmatrix}
    0 \\ 1 \\ 2 \\ 3
  \end{pmatrix} \,.
\]
Then compute the inverse transform and verify that you get back the
same vector $v$.

\item Solve the difference equation
\begin{gather*}
  t_n = 2 \, t_{n-1} + 2^{n+1} \,, \\
  t_1 = 0 \,.
\end{gather*}

\end{enumerate}
\end{document}