$$$\left[\begin{array}{cc}\sqrt{6} t & 3 t^{2}\\\sqrt{6} & 6 t\end{array}\right]$$$ 的行列式

计算 $$$\left|\begin{array}{cc}\sqrt{6} t & 3 t^{2}\\\sqrt{6} & 6 t\end{array}\right|$$$。

2x2 矩阵的行列式为 $$$\left|\begin{array}{cc}a & b\\c & d\end{array}\right| = a d - b c$$$。

$$$\left|\begin{array}{cc}\sqrt{6} t & 3 t^{2}\\\sqrt{6} & 6 t\end{array}\right| = \left(\sqrt{6} t\right)\cdot \left(6 t\right) - \left(3 t^{2}\right)\cdot \left(\sqrt{6}\right) = 3 \sqrt{6} t^{2}$$$

$$$\left|\begin{array}{cc}\sqrt{6} t & 3 t^{2}\\\sqrt{6} & 6 t\end{array}\right| = 3 \sqrt{6} t^{2}\approx 7.348469228349534 t^{2}$$$A