Question

Find the values of following determinants.

(1) $\left|\begin{array}{cc}-1& 7\\ 2& 4\end{array}\right|$


(2) $\left|\begin{array}{cc}5& 3\\ -7& 0\end{array}\right|$

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

Answer 1

(1) $\left|\begin{array}{cc}-1& 7\\ 2& 4\end{array}\right|$

= $-1\left(4\right)-7\left(2\right)=-4-14=-18$

(2) $\left|\begin{array}{cc}5& 3\\ -7& 0\end{array}\right|=5\times 0-3\times \left(-7\right)=0+21=21$

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