Question
Without expanding, show that the values of the following determinant are zero:
$\begin{vmatrix}1&43&6\\7&35&4\\3&17&2\end{vmatrix}$
$\begin{vmatrix}1&43&6\\7&35&4\\3&17&2\end{vmatrix}$
✓
Answer
$\triangle=\begin{vmatrix}1&43&6\\7&35&4\\3&17&2\end{vmatrix}$
$=\begin{vmatrix}1&1&6\\7&7&4\\3&3&2\end{vmatrix}=0$ [Appliying C2 → C2 - 7C3]
$=\begin{vmatrix}1&1&6\\7&7&4\\3&3&2\end{vmatrix}=0$ [Appliying C2 → C2 - 7C3]
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