Question

Calculate the values of the determinants:
$\left|\begin{array}{ccc}1& 1& 1\\ 35& 37& 34\\ 23& 26& 25\end{array}\right|$.

Answer 1

$\Delta =\left|\begin{array}{ccc}1& 1& 1\\ 35& 37& 34\\ 23& 26& 25\end{array}\right|C_2=C_2-C_1\Rightarrow \Delta =\left|\begin{array}{ccc}1& 0& 1\\ 35& 2& 34\\ 23& 3& 25\end{array}\right|C_3=C_3-C_1\Rightarrow \Delta =\left|\begin{array}{ccc}1& 0& 0\\ 35& 2& -1\\ 23& 3& 2\end{array}\right|$

Expanding along $R_1$

$\Rightarrow \Delta =1\{2\times 2-(-1)\times 3\}+0+0\Rightarrow \Delta =7$