Wir invertieren die Matrix ${\displaystyle {}{\begin{pmatrix}1&2\\3&-5\end{pmatrix}}}$.

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

Daher ist

${\displaystyle {}u_{1}^{*}={\frac {5}{11}}e_{1}^{*}+{\frac {2}{11}}e_{2}^{*}\,}$

und

${\displaystyle {}u_{2}^{*}={\frac {3}{11}}e_{1}^{*}-{\frac {1}{11}}e_{2}^{*}\,.}$