Question

Write the value of the determinant $\left|\begin{array}{ccc}2& -3& 5\\ 4& -6& 10\\ 6& -9& 15\end{array}\right|.$

Answer 1

$$\begin{gathered} A=\left|2-35 \\ 4-610 \\ 6-915\right| \\ =\left|2-35 \\ 4-4-6+610-10 \\ 6-915\right|\left[\mathrm{Applying}{\mathrm{R}}_2\to {\mathrm{R}}_2-2\mathrm{R}{}_1\right] \\ =\left|2-35 \\ 000 \\ 6-915\right| \\ =0 \end{gathered}$$