Question

Calculate the values of the determinants:
$\left|\begin{array}{ccc}13& 3& 23\\ 30& 7& 53\\ 39& 9& 70\end{array}\right|$.

Answer 1

$\Delta =\left|\begin{array}{ccc}13& 3& 23\\ 30& 7& 53\\ 39& 9& 70\end{array}\right|R_3=R_3-3R_1\Rightarrow \Delta =\left|\begin{array}{ccc}13& 3& 23\\ 30& 7& 53\\ 0& 0& 1\end{array}\right|$

Expanding along $R_3$

$\Rightarrow \Delta =0+0+1\{13\times 7-30\times 3\}\Rightarrow \Delta =91-90\Rightarrow \Delta =1$