Algebra-Lineare Algebra-Determinante



Beispiel Nr: 11
$ \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 $