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
A 2 × 2 determinant is \(ad - bc\). Expanding both sides:
\(\text{Left side} = x \cdot x - 18 \cdot 2 = x^2 - 36\)
\(\text{Right side} = (-4)(-4) - (-8)(-2) = 16 - 16 = 0\)
Then
\(x^2 - 36 = 0\)
\(x^2 = 36\)
So \(x = 6\) or \(x = -6\).
Checking the statements
(A) \(x = -4\) — Incorrect. \((-4)^2 = 16 \ne 36\).
(B) \(x = -6\) — Correct. \((-6)^2 = 36\).
(C) \(x = 4\) — Incorrect. \(4^2 = 16 \ne 36\).
(D) \(x = 6\) — Correct. \(6^2 = 36\).