Question

Find the value of x, if

\[\begin{vmatrix}2 & 3 \\ 4 & 5\end{vmatrix} = \begin{vmatrix}x & 3 \\ 2x & 5\end{vmatrix}\]

Answer 1

\[\text{ Given }: \begin{vmatrix}2 & 3 \\ 4 & 5\end{vmatrix} = \begin{vmatrix}x & 3 \\ 2x & 5\end{vmatrix}\]
\[ \Rightarrow 10 - 12 = 5x - 6x\]
\[ \Rightarrow - 2 = - x\]
\[ \Rightarrow x = 2\]