Question

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

Answer 1

We know that

$\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|=[ad-bc]$

$\left|\begin{array}{cc}\frac{7}{3}& \frac{5}{3}\\ \frac{3}{2}& \frac{1}{2}\end{array}\right|=\frac{7}{3}\times \frac{1}{2}-\frac{5}{3}\times \frac{3}{2}=\frac{7}{6}-\frac{5}{2}=\frac{7-15}{6}=\frac{-8}{6}=-\frac{4}{3}$