Question: Find values of x, if (i) \(\begin{vmatrix}2 & 4\\2 & 1\end{vmatrix}\) = \(\begin{vmatrix}2x & 4\\6 & x\end{vmatrix}\) (ii) \(\begin{vmatrix}2 & 3\\4 & 5\end{vmatrix}\) = \(\begin{vmatrix}x & 3\\2x & 5\end{vmatrix}\)

Answer:

(i) \(\begin{vmatrix}2 & 4\\2 & 1\end{vmatrix}\) = \(\begin{vmatrix}2x & 4\\6 & x\end{vmatrix}\)

⇒2 x 1 – 5 x 4 = 2x x x – 6 x 4)

⇒ 2- 20 = 2x² – 24

⇒2x² = 6

⇒ x² = 3

⇒ x = ±√3

(ii) \(\begin{vmatrix}2 & 3\\4 & 5\end{vmatrix}\) = \(\begin{vmatrix}x & 3\\2x & 5\end{vmatrix}\)

⇒ 2 x 5 – 3 x 4 = x x 5 – 3 x 2x

⇒10 – 12 = 5x – 6x

⇒ -2 = -x

⇒ x = 2

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