Answer
$\frac{2}{3}$
Work Step by Step
For a matrix with the following components,
[$a_{1}$ $b_{1}$
$a_{2}$ $b_{2}$],
we know that the determinant is calculated as $a_{1}b_{2}-a_{2}b_{1}$.
Therefore, the determinant for the given matrix is equal to $(\frac{2}{3})(\frac{3}{4})-(-\frac{1}{2})(\frac{1}{3})=\frac{6}{12}-(-\frac{1}{6})=\frac{6}{12}+\frac{1}{6}=\frac{6}{12}+\frac{1\times2}{6\times2}=\frac{6}{12}+\frac{2}{12}=\frac{6+2}{12}=\frac{8}{12}=\frac{2}{3}$.
