Question

Write the value of the determinant 
\[\begin{bmatrix}2 & 3 & 4 \\ 2x & 3x & 4x \\ 5 & 6 & 8\end{bmatrix} .\]

 

Answer 1

\[Let \Delta = \begin{vmatrix} 2 & 3 & 4\\ 2x & 3x & 4x \\ 5 & 6  & 8 \end{vmatrix}\] 
\[ = x\begin{vmatrix} 2 & 3 & 4\\ 2 & 3 & 4 \\ 5 & 6 & 8 \end{vmatrix} \left[\text{ Taking out x common from }R_2 \right]\] 
\[ = 0\]