Question

Without expanding, show that the value of the following determinant is zero:

\[\begin{vmatrix}49 & 1 & 6 \\ 39 & 7 & 4 \\ 26 & 2 & 3\end{vmatrix}\]

Answer 1

\[ ∆ = \begin{vmatrix}49 & 1 & 6 \\ 39 & 7 & 4 \\ 26 & 2 & 3\end{vmatrix}\]
\[ = \begin{vmatrix}1 & 1 & 6 \\ 7 & 7 & 4 \\ 2 & 2 & 3\end{vmatrix} \left[ \text{ Applying } C_1 \to C_1 - 8 C_3 \right]\]
\[ \Rightarrow ∆ = 0\]