Answer
$-\frac{7}{16}$
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 $(\frac{1}{2})(-\frac{3}{4})-(\frac{1}{8})(\frac{1}{2})=-\frac{3}{8}-\frac{1}{16}=-\frac{3\times2}{8\times2}-\frac{1}{16}=-\frac{6}{16}-\frac{1}{16}=\frac{-6-1}{16}=-\frac{7}{16}$.
