Answer
$ad-bc=\dfrac{1}{3}$
Work Step by Step
Substituting $
a=\dfrac{1}{2}
,$ $
b=-1
,$ $
c=-\dfrac{2}{3}
,$ $
d=2
$ in the expression $ad-bc,$ then
\begin{align*}\require{cancel}
&
\left( \dfrac{1}{2} \right)\left( 2 \right)-\left( -1 \right)\left( -\dfrac{2}{3} \right)
\\\\&=
1-\dfrac{2}{3}
\\\\&=
\dfrac{3}{3}-\dfrac{2}{3}
\\\\&=
\dfrac{1}{3}
.\end{align*}
Hence, $
ad-bc=\dfrac{1}{3}
$.
