Question

Find the values of each of the following determinants.

(1) $\left|\begin{array}{cc}4& 3\\ 2& 7\end{array}\right|$

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

(3) $\left|\begin{array}{cc}3& -1\\ 1& 4\end{array}\right|$

Answer 1

(1) $\left|\begin{array}{cc}4& 3\\ 2& 7\end{array}\right|=4\times 7-3\times 2=28-6=22$

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

(3) $\left|\begin{array}{cc}3& -1\\ 1& 4\end{array}\right|=3\times 4-\left(-1\right)\times 1=12+1=13$