Question

Write the value of the determinant $\left[\begin{array}{ccc}2& 3& 4\\ 2x& 3x& 4x\\ 5& 6& 8\end{array}\right].$

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{\Delta }=\left|234 \\ 2x3x4x \\ 568\right| \\ =x\left|234 \\ 234 \\ 568\right|\left[\mathrm{Taking}\mathrm{out}x\mathrm{common}\mathrm{from}{R}_2\right] \\ =0 \end{gathered}$$