Determinante von $$$\left[\begin{array}{cc}t & 3 t - 1\\1 & 3\end{array}\right]$$$

Berechne $$$\left|\begin{array}{cc}t & 3 t - 1\\1 & 3\end{array}\right|$$$.

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

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

$$$\left|\begin{array}{cc}t & 3 t - 1\\1 & 3\end{array}\right| = 1$$$A