Match List-I with List-II
| List-I | List-II | ||
| Singular matrix | A value of \( x \) | ||
| (A) | \( A=\begin{bmatrix}x & 4\\2 & 2x\end{bmatrix} \) | (I) | 3 |
| (B) | \( A=\begin{bmatrix}3 & x\\3x & 9\end{bmatrix} \) | (II) | 4 |
| (C) | \( A=\begin{bmatrix}x & 1\\1 & x\end{bmatrix} \) | (III) | 2 |
| (D) | \( A=\begin{bmatrix}x & 1\\16 & x\end{bmatrix} \) | (IV) | 1 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A) - (III), (B) - (I), (C) - (IV), (D) - (II)
A matrix is singular when its determinant is 0.
(A) \( \begin{bmatrix}x & 4\\2 & 2x\end{bmatrix} \)
This matches (III) 2.
\( \displaystyle 2x^2-8=0 \)
\( \displaystyle x=\pm 2 \)
(B) \( \begin{bmatrix}3 & x\\3x & 9\end{bmatrix} \)
This matches (I) 3.
\( \displaystyle 27-3x^2=0 \)
\( \displaystyle x=\pm 3 \)
(C) \( \begin{bmatrix}x & 1\\1 & x\end{bmatrix} \)
This matches (IV) 1.
\( \displaystyle x^2-1=0 \)
\( \displaystyle x=\pm 1 \)
(D) \( \begin{bmatrix}x & 1\\16 & x\end{bmatrix} \)
This matches (II) 4.
\( \displaystyle x^2-16=0 \)
\( \displaystyle x=\pm 4 \)
Each matrix has two such values (±); List-II gives the positive one.
So the matching is (A)-(III), (B)-(I), (C)-(IV), (D)-(II).