Question

Find the value of the following determinants.
$\left|\begin{array}{cc}\frac{7}{3}& \frac{5}{3}\\ \frac{3}{2}& \frac{1}{2}\end{array}\right|$

Answer 1

$\left|\begin{array}{cc}\frac{7}{3}& \frac{5}{3}\\ \frac{3}{2}& \frac{1}{2}\end{array}\right|$

$=\left(\frac{7}{3}\right)\left(\frac{1}{2}\right)-\left(\frac{5}{3}\right)\left(\frac{3}{2}\right)$

$\Rightarrow \frac{7}{6}-\frac{15}{6}=\frac{-8}{6}=\frac{-4}{3}$