Answer
$-\dfrac{7}{16}$
Work Step by Step
General formula to calculate the determinate of a matrix is:
$D=\begin{vmatrix}p&q\\r&s\end{vmatrix}=ps-qr$
As per question, we have
Thus, $D=\begin{vmatrix}\frac{1}{2}&\frac{1}{2}\\\frac{1}{8}&\frac{-3}{4}\end{vmatrix}$
or, $D=\dfrac{-3}{8}-\dfrac{1}{16}=-\dfrac{7}{16}$
