Algebra-Lineare Algebra-Determinante
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$Determinante$
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Beispiel Nr: 11
$\begin{array}{l}
\text{Gegeben: } D=\left|\begin{array}{ccc}
a1\ & b1 & c1\\
a2&b2 & c2\\
a3& b3 & c3
\end{array}\right| \\
\\
\\ \text{Gesucht: } \\\text{ Wert der Determinante D }
\\ \\ \textbf{Gegeben:} \\
D=\left|\begin{array}{ccc}
\frac{14}{15}\ & 2\frac{4}{5} & 1\\
1\frac{6}{13}&1\frac{1}{2} & 19\\
1\frac{3}{8}& \frac{5}{16} & \frac{1}{11}
\end{array}\right|
\\ \\ \textbf{Rechnung:} \\
D=\left|\begin{array}{ccc}
\frac{14}{15}\ & 2\frac{4}{5} & 1\\
1\frac{6}{13}&1\frac{1}{2} & 19\\
1\frac{3}{8}& \frac{5}{16} & \frac{1}{11} \\
\end{array}\right|
\begin{array}{cc}
\frac{14}{15}\ & 2\frac{4}{5} \\
1\frac{6}{13}&1\frac{1}{2} \\
1\frac{3}{8}& \frac{5}{16}
\end{array} \\
D=\frac{14}{15} \cdot 1\frac{1}{2} \cdot \frac{1}{11}+ 2\frac{4}{5} \cdot 19 \cdot 1\frac{3}{8} + 1 \cdot 1\frac{6}{13} \cdot \frac{5}{16} \\
- 1 \cdot 1\frac{1}{2} \cdot 1\frac{3}{8} - \frac{14}{15} \cdot 19 \cdot \frac{5}{16} - 2\frac{4}{5} \cdot 1\frac{6}{13} \cdot \frac{1}{11}=65,8
\end{array}$