Question

Calculate the values of the determinants:
$\left|\begin{array}{ccc}13& 16& 19\\ 14& 17& 20\\ 15& 18& 21\end{array}\right|$

Answer 1

$\Delta =\left|\begin{array}{ccc}13& 16& 19\\ 14& 17& 20\\ 15& 18& 21\end{array}\right|R_1=R_1-R_2\Rightarrow \Delta =\left|\begin{array}{ccc}-1& -1& -1\\ 14& 17& 20\\ 15& 18& 21\end{array}\right|R_2=R_2-R_3\Rightarrow \Delta =\left|\begin{array}{ccc}-1& -1& -1\\ -1& -1& -1\\ 15& 18& 21\end{array}\right|$

Two rows of the determinant are same

$\Rightarrow \Delta =0$