Determinante von $$$\left[\begin{array}{cc}x & x^{5}\\1 & 5 x^{4}\end{array}\right]$$$

Berechne $$$\left|\begin{array}{cc}x & x^{5}\\1 & 5 x^{4}\end{array}\right|$$$.

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

$$$\left|\begin{array}{cc}x & x^{5}\\1 & 5 x^{4}\end{array}\right| = \left(x\right)\cdot \left(5 x^{4}\right) - \left(x^{5}\right)\cdot \left(1\right) = 4 x^{5}$$$

$$$\left|\begin{array}{cc}x & x^{5}\\1 & 5 x^{4}\end{array}\right| = 4 x^{5}$$$A