Question

Find the value of the following determinant :

(i) $\left|\begin{array}{cc}5& 2\\ 7& 4\end{array}\right|$

(ii) $\left|\begin{array}{cc}-3& 8\\ 6& 0\end{array}\right|$

(iii) $\left|\begin{array}{cc}1.2& 0.03\\ 0.57& -0.23\end{array}\right|$

(iv) $\left|\begin{array}{cc}3\sqrt{6}& -4\sqrt{2}\\ 5\sqrt{3}& 2\end{array}\right|$

(v) $\left|\begin{array}{cc}\frac{-4}{7}& \frac{-6}{35}\\ 5& \frac{-2}{5}\end{array}\right|$

Answer 1

(i) $\left|\begin{array}{cc}5& 2\\ 7& 4\end{array}\right|$ = $\left(5\times 4\right)-\left(2\times 7\right)=20-14=6$

(ii) $\left|\begin{array}{cc}-3& 8\\ 6& 0\end{array}\right|$ = $\left(-3\times 0\right)-\left(8\times 6\right)=0-48=-48$

(iii) $\left|\begin{array}{cc}1.2& 0.03\\ 0.57& -0.23\end{array}\right|$ = $\left(1.2\times -0.23\right)-\left(0.03\times 0.57\right)=-0.276-0.0171=-0.2931$

(iv) $\left|\begin{array}{cc}3\sqrt{6}& -4\sqrt{2}\\ 5\sqrt{3}& 2\end{array}\right|$ = $\left(3\sqrt{6}\times 2\right)-\left(-4\sqrt{2}\times 5\sqrt{3}\right)=6\sqrt{6}+20\sqrt{6}=26\sqrt{6}$

(v) $\left|\begin{array}{cc}\frac{-4}{7}& \frac{-6}{35}\\ 5& \frac{-2}{5}\end{array}\right|$ = $\left(\frac{-4}{7}\times \frac{-2}{5}\right)-\left(\frac{-6}{35}\times 5\right)=\frac{8}{35}+\frac{30}{35}=\frac{38}{35}$