Question

Evaluate :
${\left|\begin{array}{ccc}2& 3& 7\\ 13& 17& 5\\ 15& 20& 12\end{array}\right|}^2$

Answer 1

$\left|\begin{array}{ccc}2& 3& 7\\ 13& 17& 5\\ 15& 20& 12\end{array}\right|$

[$R_3^{\prime }=R_3-R_2$]

$=\left|\begin{array}{ccc}2& 3& 7\\ 13& 17& 5\\ 2& 3& 7\end{array}\right|$

$=0$ (Since first and last rows are same).

$\therefore$${\left|\begin{array}{ccc}2& 3& 7\\ 13& 17& 5\\ 15& 20& 12\end{array}\right|}^2=0^2=0$.