Let $\begin{vmatrix}x&2\\18&x\end{vmatrix}=\begin{vmatrix}-4&-2\\-8&-4\end{vmatrix}$. Then
(A) $x = -4$
(B) $x = -6$
(C) $x = 4$
(D) $x = 6$
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (B) and (D) only
Given:
$\begin{vmatrix} x & 2 \\ 18 & x \end{vmatrix} = \begin{vmatrix} -4 & -2 \\ -8 & -4 \end{vmatrix}$
Evaluate both determinants.
Left side:
$x\cdot x - 18\cdot 2 = x^{2} - 36$
Right side:
$(-4)(-4) - (-8)(-2) = 16 - 16 = 0$
Hence:
$x^{2} - 36 = 0$
$x^{2} = 36$
$x = \pm 6$
From options, $x=-6$ and $x=6$ satisfy.
Final answer: $x=-6$ and $x=6$