Question

Evaluate the following determinants without expansion as far as possible.
$\left|\begin{array}{ccc}13& 1& 6\\ 35& 7& 4\\ 17& 3& 2\end{array}\right|$

Answer 1

$△$ = $
\left |
\begin{array}{111}
7.6 +1 & 1 & 6 \\
7.4+7 & 7 & 4 \\
7.2+3 & 3 & 2 \\
\end {array}
\right |
$
= 7 $
\left |
\begin{array}{111}
6 & 1 & 6 \\
4 & 7 & 4 \\
2 & 3 & 2 \\
\end{array}
\right |
$+$
\left |
\begin{array}{111}
1 & 1 & 6 \\
7 & 7 & 4 \\
3 & 3 & 2 \\
\end {array}
\right |
$
= 7.0+0 =0.
Both the determinants are zero because of identical columns.
Aliter: Apply $C_1-7C_3$ the $C_1$ and $C_2$ are identical $\therefore △=0$