Determinante von $$$\left[\begin{array}{cc}x & x^{3}\\1 & 3 x^{2}\end{array}\right]$$$

Berechne $$$\left|\begin{array}{cc}x & x^{3}\\1 & 3 x^{2}\end{array}\right|$$$.

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

$$$\left|\begin{array}{cc}x & x^{3}\\1 & 3 x^{2}\end{array}\right| = \left(x\right)\cdot \left(3 x^{2}\right) - \left(x^{3}\right)\cdot \left(1\right) = 2 x^{3}$$$

$$$\left|\begin{array}{cc}x & x^{3}\\1 & 3 x^{2}\end{array}\right| = 2 x^{3}$$$A