Question

Evaluate $\left|\begin{array}{ccc}13& 16& 19\\ 14& 17& 20\\ 15& 18& 21\end{array}\right|$

Answer 1

$\left|\begin{array}{ccc}13& 16& 19\\ 14& 17& 20\\ 15& 18& 21\end{array}\right|$
Applying $R_2\to R_2-R_1$ and $R_3\to R_3-R_1$
$\left|\begin{array}{ccc}13& 16& 19\\ 1& 1& 1\\ 2& 2& 2\end{array}\right|$
$=0$ ($\because R_2$ and $R_3$ are proportional)