Question: Evaluate $\left|\begin{array}{cc}\sqrt{3} & \sqrt{5} \\ -\sqrt{5} & 3 \sqrt{3}\end{array}\right|$
Solution:
$\left|\begin{array}{cc}\sqrt{3} & \sqrt{5} \\ -\sqrt{5} & 3 \sqrt{3}\end{array}\right|=3 \sqrt{3} \times \sqrt{3}-(-\sqrt{5} \times \sqrt{5})$
$=14$
