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\firstpageheader{Scientific Computing}{Matrix multiplication}{Oct 28, 2014}
%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
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\begin{document}

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%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%

\begin{questions}
  \question \textbf{Matrix multiplication} 
  Calculate the results of the following matrix multiplications and
  confirm the result using matlab.
    \[ \begin{pmatrix} 2 \\ -4 \\ -1 \end{pmatrix} \cdot
    \begin{pmatrix} 3 & -4 & -4 \end{pmatrix} = \]

    \[ \begin{pmatrix} 3 & -3 & -1 \end{pmatrix} \cdot
    \begin{pmatrix} 2 \\ 3 \\ 0 \end{pmatrix} = \]

    \[ \begin{pmatrix} 4 & -1 & 2 \\ -1 & 3 & 1 \\ 4 & -2 & 1 \\ 4 & -3 & -2 \end{pmatrix} \cdot
    \begin{pmatrix} -2 & -2 & 0 & -3 \\ 3 & -2 & 1 & 0 \\ 1 & -2 & -4 & 0 \end{pmatrix} = \]

    \[ \begin{pmatrix} 3 & 1 \\ 1 & 4 \end{pmatrix} \cdot
    \begin{pmatrix} 0 & -3 & 4 & 1 \\ -2 & -1 & -2 & -3 \\ -3 & 1 & -2 & -3 \end{pmatrix} = \]

    \[ \begin{pmatrix} 1 & 1 & -4 \end{pmatrix} \cdot
    \begin{pmatrix} -1 \\ 2 \end{pmatrix} = \]

    \[ \begin{pmatrix} 3 & 1 & -2 \\ 2 & 1 & 3 \\ 1 & 1 & 2 \end{pmatrix} \cdot
    \begin{pmatrix} 2 & 2 \\ -3 & 3 \\ -4 & 1 \end{pmatrix} = \]

    \[ \begin{pmatrix} 3 \\ 2 \end{pmatrix} \cdot
    \begin{pmatrix} -3 & 2 & -4 & 1 \end{pmatrix} = \]

    \[ \begin{pmatrix} -1 \\ -4 \\ -1 \end{pmatrix} \cdot
    \begin{pmatrix} 0 & -4 & 1 \end{pmatrix} = \]

    \[ \begin{pmatrix} 4 & -2 & -2 & -4 \end{pmatrix} \cdot
    \begin{pmatrix} 2 \\ 2 \\ 1 \\ -1 \end{pmatrix} = \]

    \[ \begin{pmatrix} -2 & -3 & -4 \\ 1 & 3 & 2 \\ -4 & -2 & 1 \end{pmatrix} \cdot
    \begin{pmatrix} 1 & 2 & -2 & 4 \\ 3 & -1 & 1 & -1 \\ -3 & 2 & -1 & 2 \end{pmatrix} = \]

   \[ \begin{pmatrix} 2 & -4 & 4 & 4 \\ -3 & 3 & 2 & 1 \end{pmatrix} \cdot
    \begin{pmatrix} 0 & 3 & 4 & -2 \\ -4 & -2 & -1 & 0 \\ 1 & 2 & -4 & -4 \\ 3 & 2 & -2 & -4 \end{pmatrix} = \]

    \[ \begin{pmatrix} 3 & 1 & -2 & -2 \end{pmatrix} \cdot
    \begin{pmatrix} -4 \\ 3 \\ -2 \\ 4 \end{pmatrix} = \]

    \[ \begin{pmatrix} -1 & 3 & 4 \end{pmatrix} \cdot
    \begin{pmatrix} -1 \\ 4 \\ -3 \end{pmatrix} = \]

    \[ \begin{pmatrix} 1 & -4 & 3 & 3 \end{pmatrix} \cdot
    \begin{pmatrix} 1 \\ 0 \\ -4 \\ -1 \end{pmatrix} = \]

    \[ \begin{pmatrix} -4 & -4 & -3 \\ -2 & -2 & 4 \\ -3 & 4 & -3 \end{pmatrix} \cdot
    \begin{pmatrix} 0 & 3 & -4 & 4 \\ -1 & -2 & -3 & 1 \\ 1 & -2 & 2 & 0 \end{pmatrix} = \]

    \[ \begin{pmatrix} -3 & 0 & 4 & 1 \\ 0 & 1 & 1 & 4 \end{pmatrix} \cdot
    \begin{pmatrix} -4 & 3 & 1 & 4 \\ 1 & -4 & 1 & -3 \\ -4 & 0 & -4 & -4 \\ 1 & -2 & 4 & 4 \end{pmatrix} = \]

    \[ \begin{pmatrix} 4 \\ 3 \\ 4 \\ -2 \end{pmatrix} \cdot
    \begin{pmatrix} 2 & 4 & 3 & 3 \end{pmatrix} = \]

    \[ \begin{pmatrix} 1 & 2 & 0 & 3 \end{pmatrix} \cdot
    \begin{pmatrix} -3 \\ 1 \\ 1 \end{pmatrix} = \]

    \[ \begin{pmatrix} -4 & 0 & -1 & 3 \\ 0 & -4 & 3 & -3 \end{pmatrix} \cdot
    \begin{pmatrix} -1 & -4 & -1 \\ 3 & 2 & 0 \\ -2 & 3 & -2 \\ 1 & 2 & -2 \end{pmatrix} = \]

    \[ \begin{pmatrix} 2 & 0 & 3 \\ 1 & -4 & -1 \\ 3 & 0 & -2 \end{pmatrix} \cdot
    \begin{pmatrix} 0 & 2 & -1 & -2 \\ -1 & -1 & -3 & 4 \\ 2 & 4 & -4 & 1 \end{pmatrix} = \]
    \[ \begin{pmatrix} -1 & 4 \end{pmatrix} \cdot
    \begin{pmatrix} 0 \\ 1 \end{pmatrix} = \]

    \[ \begin{pmatrix} -4 & 3 \\ -4 & 0 \\ -2 & -2 \end{pmatrix} \cdot
    \begin{pmatrix} 0 & 1 & -4 & 2 \\ 2 & 3 & -2 & -1 \end{pmatrix} = \]

    \[ \begin{pmatrix} -2 & -1 \end{pmatrix} \cdot
    \begin{pmatrix} 1 \\ -2 \end{pmatrix} = \]

    \[ \begin{pmatrix} -2 & 2 & -2 & -3 \\ 2 & -4 & -2 & 2 \\ 0 & 2 & -2 & -2 \\ 1 & -2 & -2 & -2 \end{pmatrix} \cdot
    \begin{pmatrix} 1 & -2 & 2 \\ -4 & -2 & -2 \\ 3 & 1 & 4 \\ -4 & 1 & -2 \end{pmatrix} = \]

    \[ \begin{pmatrix} -1 & -3 & 0 & -1 \\ 4 & -2 & 1 & 2 \end{pmatrix} \cdot
    \begin{pmatrix} -3 & -4 \\ -4 & 0 \end{pmatrix} = \]

    \[ \begin{pmatrix} -1 & 1 & -2 \\ -2 & 2 & -4 \\ 1 & -2 & -2 \end{pmatrix} \cdot
    \begin{pmatrix} -1 & 2 & -4 \\ 1 & 3 & 0 \\ 1 & 4 & -4 \end{pmatrix} = \]

    \[ \begin{pmatrix} -3 & 3 \\ -3 & 2 \end{pmatrix} \cdot
    \begin{pmatrix} 2 & -3 \\ -2 & -4 \end{pmatrix} = \]

    \[ \begin{pmatrix} 1 & 1 & -3 \end{pmatrix} \cdot
    \begin{pmatrix} -1 \\ -2 \\ 3 \end{pmatrix} = \]

    \[ \begin{pmatrix} -4 & 2 & 1 \\ 4 & 0 & -2 \\ 2 & 3 & -3 \\ -2 & -2 & -2 \end{pmatrix} \cdot
    \begin{pmatrix} -1 & 2 & 0 & -2 \\ 2 & -2 & 0 & -1 \\ -4 & 3 & -3 & 4 \end{pmatrix} = \]

    \[ \begin{pmatrix} -2 & -4 & 2 & 4 \\ 3 & -3 & 2 & 1 \end{pmatrix} \cdot
    \begin{pmatrix} 0 & 4 & -1 & -4 \\ 2 & 3 & -4 & -1 \\ 3 & 2 & -2 & 4 \end{pmatrix} = \]

   \[ \begin{pmatrix} -3 & -2 & -1 & -3 \end{pmatrix} \cdot
    \begin{pmatrix} 2 \\ -2 \\ 3 \\ -2 \end{pmatrix} = \]

    \[ \begin{pmatrix} 4 & 4 & 2 & 3 \end{pmatrix} \cdot
    \begin{pmatrix} 3 \\ 3 \\ -2 \\ 1 \end{pmatrix} = \]

    \[ \begin{pmatrix} 3 & 2 & -2 \end{pmatrix} \cdot
    \begin{pmatrix} 2 \\ 4 \\ 3 \end{pmatrix} = \]

    \[ \begin{pmatrix} 2 & -1 & 0 & -2 \\ 0 & -4 & -3 & -1 \end{pmatrix} \cdot
    \begin{pmatrix} 4 & -3 & 2 & 4 \\ -3 & -4 & 1 & 1 \\ 1 & 3 & -2 & 3 \\ -1 & -2 & 3 & 0 \end{pmatrix} = \]

    \[ \begin{pmatrix} -3 & -3 & 3 & 2 \\ 2 & 2 & -3 & 1 \end{pmatrix} \cdot
    \begin{pmatrix} 0 & 1 \\ 4 & 2 \\ -3 & -1 \\ -3 & 4 \end{pmatrix} = \]

    \[ \begin{pmatrix} -4 & -3 \end{pmatrix} \cdot
    \begin{pmatrix} -2 \\ 3 \\ 4 \end{pmatrix} = \]

    \[ \begin{pmatrix} 4 & 4 \end{pmatrix} \cdot
    \begin{pmatrix} 1 \\ 4 \\ -1 \end{pmatrix} = \]

    \[ \begin{pmatrix} 1 & -2 & 3 \end{pmatrix} \cdot
    \begin{pmatrix} 3 \\ 1 \\ 2 \end{pmatrix} = \]

    \[ \begin{pmatrix} -3 & 2 \end{pmatrix} \cdot
    \begin{pmatrix} -1 \\ 1 \end{pmatrix} = \]

    \[ \begin{pmatrix} -2 & -4 & -4 & 0 \\ 0 & 3 & 4 & -4 \\ 4 & 2 & -2 & -4 \\ 0 & 0 & 4 & -1 \end{pmatrix} \cdot
    \begin{pmatrix} 0 & -1 \\ -1 & 1 \\ -4 & -3 \\ 2 & 1 \end{pmatrix} = \]

    \[ \begin{pmatrix} -3 \\ 3 \\ -3 \\ -4 \end{pmatrix} \cdot
    \begin{pmatrix} 2 & 4 & -2 & 1 \end{pmatrix} = \]

    \[ \begin{pmatrix} 2 \\ 0 \end{pmatrix} \cdot
    \begin{pmatrix} -1 & -3 & -2 & 2 \end{pmatrix} = \]

    \[ \begin{pmatrix} 0 & -4 & -4 & 4 \end{pmatrix} \cdot
    \begin{pmatrix} 1 \\ 4 \\ 0 \\ 4 \end{pmatrix} = \]

    \[ \begin{pmatrix} -3 & -1 \\ -3 & -1 \end{pmatrix} \cdot
    \begin{pmatrix} 0 & -3 & 3 & -2 \\ -4 & 1 & -1 & 4 \end{pmatrix} = \]

    \[ \begin{pmatrix} 4 & 0 \\ -1 & 4 \\ 1 & -3 \end{pmatrix} \cdot
    \begin{pmatrix} -4 & -4 \\ -4 & 2 \end{pmatrix} = \]

    \[ \begin{pmatrix} -1 \\ 3 \\ 2 \\ 4 \end{pmatrix} \cdot
    \begin{pmatrix} 0 & -1 & 0 & 0 \end{pmatrix} = \]

    \[ \begin{pmatrix} 3 \\ -2 \\ 2 \\ 3 \end{pmatrix} \cdot
    \begin{pmatrix} -2 & -3 & -4 & 2 \end{pmatrix} = \]

    \[ \begin{pmatrix} 2 & -2 & -4 & 4 \\ 0 & 1 & -3 & -2 \\ -1 & 3 & 0 & -2 \end{pmatrix} \cdot
    \begin{pmatrix} -4 & 1 \\ -4 & 3 \end{pmatrix} = \]

    \[ \begin{pmatrix} -4 & -1 & 3 \end{pmatrix} \cdot
    \begin{pmatrix} -4 \\ -3 \\ 3 \end{pmatrix} = \]

  \question \textbf{Automatic generation of exercises}
  Write some matlab code that generates exercises like this one automatically! :-) 
  
\end{questions}


\end{document}
