Einführung in das mathematische Arbeiten

\begin{gather*} A_{1} := \begin{pmatrix} 1 & 1 & 1\\0 & 1 & 2\\2 & \;3\; & \;4\; \end{pmatrix},\quad A_{2} := \begin{pmatrix} 1 & 2 & 4\\1 & 3 & 5\\\;2\; & \;1\; & -1 \end{pmatrix},\quad A_{3} := \begin{pmatrix} 3 & 0 & 0\\ 0 & -2 & 0\\\;0\; & \;0\; & \;4\; \end{pmatrix}, \end{gather*}

\begin{gather*} x_{1} := \begin{pmatrix} 3\\1\\2 \end{pmatrix},\quad x_{2} := \begin{pmatrix} -1\\2\\4 \end{pmatrix},\quad x_{3} := \begin{pmatrix} 0\\1\\0 \end{pmatrix}. \end{gather*}

\begin{gather*} A_1+A_1 = \begin{pmatrix}2&2&2\\0&2&4\\4&6&8\end{pmatrix},\quad A_1+A_2 = \begin{pmatrix}2&3&5\\1&4&7\\4&4&3\end{pmatrix},\quad A_1+A_3 = \begin{pmatrix}4&1&1\\0&-1&2\\2&3&8\end{pmatrix},\\ A_2+A_2 = \begin{pmatrix}2&4&8\\2&6&10\\4&2&-2\end{pmatrix},\quad A_2+A_3 = \begin{pmatrix}4&2&4\\1&1&5\\2&1&3\end{pmatrix},\quad A_3+A_3 = \begin{pmatrix}6&0&0\\0&-4&0\\0&0&8\end{pmatrix},\\ A_1A_1 = \begin{pmatrix}3&5&7\\4&7&10\\10&17&24\end{pmatrix},\quad A_1A_2 = \begin{pmatrix}4&6&8\\5&5&3\\13&17&19\end{pmatrix},\quad A_1A_3 = \begin{pmatrix}3&-2&4\\0&-2&8\\6&-6&16\end{pmatrix},\\ A_2A_1 = \begin{pmatrix}9&15&21\\11&19&27\\0&0&0\end{pmatrix},\quad A_2A_2 = \begin{pmatrix}11&12&10\\14&16&14\\1&6&14\end{pmatrix},\quad A_2A_3 = \begin{pmatrix}3&-4&16\\3&-6&20\\6&-2&-4\end{pmatrix},\\ A_3A_1 = \begin{pmatrix}3&-4&16\\3&-6&20\\6&-2&-4\end{pmatrix},\quad A_3A_2 = \begin{pmatrix}3&6&12\\-2&-6&-10\\8&4&-4\end{pmatrix},\quad A_3A_3 = \begin{pmatrix}9&0&0\\0&4&0\\0&0&16\end{pmatrix},\\ A_1x_1 = \begin{pmatrix}6\\5\\17\end{pmatrix},\quad A_1x_2 = \begin{pmatrix}5\\10\\20\end{pmatrix},\quad A_1x_3 = \begin{pmatrix}1\\1\\3\end{pmatrix},\\ A_2x_1 = \begin{pmatrix}13\\16\\5\end{pmatrix},\quad A_2x_2 = \begin{pmatrix}19\\25\\-4\end{pmatrix},\quad A_2x_3 = \begin{pmatrix}2\\3\\1\end{pmatrix},\\ A_3x_1 = \begin{pmatrix}9\\-2\\8\end{pmatrix},\quad A_3x_2 = \begin{pmatrix}-3\\-4\\16\end{pmatrix},\quad A_3x_3 = \begin{pmatrix}0\\-2\\0\end{pmatrix}. \end{gather*}