Algebra-Lineare Algebra-Determinante
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$Determinante$
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Beispiel Nr: 12
$\begin{array}{l}
\text{Gegeben: } D=\left|\begin{array}{ccc}
a1\ & b1 & c1\\
a2&b2 & c2\\
a3& b3 & c3
\end{array}\right| \\
\\
\\ \text{Gesucht: } \\\text{ Wert der Determinante D }
\\ \\ \textbf{Gegeben:} \\
D=\left|\begin{array}{ccc}
\frac{1}{17}\ & 14 & \frac{1}{4}\\
1\frac{2}{17}&\frac{1}{3} & 6\frac{1}{2}\\
\frac{2}{3}& \frac{8}{11} & \frac{8}{17}
\end{array}\right|
\\ \\ \textbf{Rechnung:} \\
D=\left|\begin{array}{ccc}
\frac{1}{17}\ & 14 & \frac{1}{4}\\
1\frac{2}{17}&\frac{1}{3} & 6\frac{1}{2}\\
\frac{2}{3}& \frac{8}{11} & \frac{8}{17} \\
\end{array}\right|
\begin{array}{cc}
\frac{1}{17}\ & 14 \\
1\frac{2}{17}&\frac{1}{3} \\
\frac{2}{3}& \frac{8}{11}
\end{array} \\
D=\frac{1}{17} \cdot \frac{1}{3} \cdot \frac{8}{17}+ 14 \cdot 6\frac{1}{2} \cdot \frac{2}{3} + \frac{1}{4} \cdot 1\frac{2}{17} \cdot \frac{8}{11} \\
- \frac{1}{4} \cdot \frac{1}{3} \cdot \frac{2}{3} - \frac{1}{17} \cdot 6\frac{1}{2} \cdot \frac{8}{11} - 14 \cdot 1\frac{2}{17} \cdot \frac{8}{17}=53,2
\end{array}$