Question

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

\[\begin{vmatrix}1 & 43 & 6 \\ 7 & 35 & 4 \\ 3 & 17 & 2\end{vmatrix}\]

Answer 1

\[ ∆ = \begin{vmatrix}1 & 43 & 6 \\ 7 & 35 & 4 \\ 3 & 17 & 2\end{vmatrix}\]
\[ = \begin{vmatrix}1 & 1 & 6 \\ 7 & 7 & 4 \\ 3 & 3 & 2\end{vmatrix} = 0 \left[ \text{ Applying }C_2 \to C_2 - 7 C_3 \right]\]