Question

Find the value of x, if
\[\begin{vmatrix}2 & 4 \\ 5 & 1\end{vmatrix} = \begin{vmatrix}2x & 4 \\ 6 & x\end{vmatrix}\]

Answer 1

\[\text{ Given }: \hspace{0.167em} \begin{vmatrix}2 & 4 \\ 5 & 1\end{vmatrix} = \begin{vmatrix}2x & 4 \\ 6 & x\end{vmatrix}\]
\[ \Rightarrow 2 - 20 = 2 x^2 - 24\]
\[ \Rightarrow - 18 = 2 x^2 - 24\]
\[ \Rightarrow 2 x^2 = 6\]
\[ \Rightarrow x^2 = 3\]
\[ \Rightarrow x = \pm \sqrt{3}\]