Question

Write the value of the determinant $\left|\begin{array}{ccc}2& 3& 4\\ 5& 6& 8\\ 6x& 9x& 12x\end{array}\right|$

Answer 1

$$\begin{gathered} \left|\begin{array}{ccc}2& 3& 4\\ 5& 6& 8\\ 6x& 9x& 12x\end{array}\right| \\ =\left|\begin{array}{ccc}2& 3& 4\\ 5& 6& 8\\ 2& 3& 4\end{array}\right|\left[\mathrm{Taking}2x\mathrm{common}\mathrm{from}{R}_3\right] \\ =0\left[\because R_1\mathrm{and}{R}_3\mathrm{are}\mathrm{identical}\right] \end{gathered}$$