Question

The value of \( x \), for which the matrix \( A \) is singular, is: \[ A = \begin{pmatrix} 2 & x & -1 & 2 \\ 1 & x & 2x^2 \\ 1 & \frac{1}{x} & 2 \end{pmatrix} \]

• A. \( \pm 1 \)
• B. \( \pm 2 \)
• C. \( \pm 3 \)
• D. \( \pm 4 \)

Hint:

A matrix is singular if its determinant equals zero. For this matrix, solving the determinant yields \( x = \pm 1 \).

Answer 1

The Correct Option is A

Step 1: Condition for singularity. A matrix is singular if its determinant is zero. We need to calculate the determinant of matrix \( A \) and set it equal to zero.
Step 2: Conclusion. After solving the determinant, we find that \( x = \pm 1 \).