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# Invertierbare Matrix/Finden der inversen Matrix/Tabelle/Verfahren/131/412/011/Beispiel

Wir wollen zur Matrix ${\displaystyle {}{\begin{pmatrix}1&3&1\\4&1&2\\0&1&1\end{pmatrix}}}$ gemäß dem in Fakt beschriebenen Verfahren die inverse Matrix ${\displaystyle {}M^{-1}}$ bestimmen.

${\displaystyle {}{\begin{pmatrix}1&3&1\\4&1&2\\0&1&1\end{pmatrix}}}$ ${\displaystyle {}{\begin{pmatrix}1&0&0\\0&1&0\\0&0&1\end{pmatrix}}}$
${\displaystyle {}{\begin{pmatrix}1&3&1\\0&-11&-2\\0&1&1\end{pmatrix}}}$ ${\displaystyle {}{\begin{pmatrix}1&0&0\\-4&1&0\\0&0&1\end{pmatrix}}}$
${\displaystyle {}{\begin{pmatrix}1&3&1\\0&1&1\\0&-11&-2\end{pmatrix}}}$ ${\displaystyle {}{\begin{pmatrix}1&0&0\\0&0&1\\-4&1&0\end{pmatrix}}}$
${\displaystyle {}{\begin{pmatrix}1&3&1\\0&1&1\\0&0&9\end{pmatrix}}}$ ${\displaystyle {}{\begin{pmatrix}1&0&0\\0&0&1\\-4&1&11\end{pmatrix}}}$
${\displaystyle {}{\begin{pmatrix}1&3&1\\0&1&1\\0&0&1\end{pmatrix}}}$ ${\displaystyle {}{\begin{pmatrix}1&0&0\\0&0&1\\{\frac {-4}{9}}&{\frac {1}{9}}&{\frac {11}{9}}\end{pmatrix}}}$
${\displaystyle {}{\begin{pmatrix}1&0&-2\\0&1&1\\0&0&1\end{pmatrix}}}$ ${\displaystyle {}{\begin{pmatrix}1&0&-3\\0&0&1\\{\frac {-4}{9}}&{\frac {1}{9}}&{\frac {11}{9}}\end{pmatrix}}}$
${\displaystyle {}{\begin{pmatrix}1&0&0\\0&1&0\\0&0&1\end{pmatrix}}}$ ${\displaystyle {}{\begin{pmatrix}{\frac {1}{9}}&{\frac {2}{9}}&{\frac {-5}{9}}\\{\frac {4}{9}}&{\frac {-1}{9}}&{\frac {-2}{9}}\\{\frac {-4}{9}}&{\frac {1}{9}}&{\frac {11}{9}}\end{pmatrix}}}$