Evaluate the following determinant: 102&18&36 1&3&4 17&3&6 - Vidyadip

Question

Evaluate the following determinant:
$\begin{vmatrix}102&18&36\\1&3&4\\17&3&6\end{vmatrix}$

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Answer

Let $\triangle=\begin{vmatrix}102&18&36\\1&3&4\\17&3&6\end{vmatrix}$
Applying $R_3 → 17R_2 - R_3$, we get
$\triangle=\begin{vmatrix}102&18&36\\1&3&4\\0&48&62\end{vmatrix}$
Applying $R_2 → 102R_2 - R_1$, we get
$\triangle=\begin{vmatrix}102&18&36\\0&288&327\\0&48&62\end{vmatrix}$
Thus, $\triangle=102(288\times62-372\times48)$
$\triangle=0$

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