Determinante von $$$\left[\begin{array}{cc}2 \cos{\left(5 v \right)} & - 10 u \sin{\left(5 v \right)}\\0 & 10 \cos{\left(5 v \right)}\end{array}\right]$$$

Der Rechner berechnet die Determinante der quadratischen $$$2$$$x$$$2$$$-Matrix $$$\left[\begin{array}{cc}2 \cos{\left(5 v \right)} & - 10 u \sin{\left(5 v \right)}\\0 & 10 \cos{\left(5 v \right)}\end{array}\right]$$$, wobei die Rechenschritte angezeigt werden.

Verwandter Rechner: Kofaktormatrix-Rechner

Ihre Eingabe

Berechne $$$\left|\begin{array}{cc}2 \cos{\left(5 v \right)} & - 10 u \sin{\left(5 v \right)}\\0 & 10 \cos{\left(5 v \right)}\end{array}\right|$$$.

Lösung

Die Determinante einer 2x2-Matrix ist $$$\left|\begin{array}{cc}a & b\\c & d\end{array}\right| = a d - b c$$$.

$$$\left|\begin{array}{cc}2 \cos{\left(5 v \right)} & - 10 u \sin{\left(5 v \right)}\\0 & 10 \cos{\left(5 v \right)}\end{array}\right| = \left(2 \cos{\left(5 v \right)}\right)\cdot \left(10 \cos{\left(5 v \right)}\right) - \left(- 10 u \sin{\left(5 v \right)}\right)\cdot \left(0\right) = 20 \cos^{2}{\left(5 v \right)}$$$

Antwort

$$$\left|\begin{array}{cc}2 \cos{\left(5 v \right)} & - 10 u \sin{\left(5 v \right)}\\0 & 10 \cos{\left(5 v \right)}\end{array}\right| = 20 \cos^{2}{\left(5 v \right)}$$$A

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