Question

If \[ A= \begin{bmatrix} 3 & x & 2\\ 2x & 3 & -1\\ 1 & 2 & 3x \end{bmatrix} \] is a singular matrix and \(x\gt 0\), then \(\sqrt{3}\,x=\)

• A. \(\sqrt{21}\)
• B. \(\sqrt{11}\)
• C. \(\sqrt{13}\)
• D. \(\sqrt{17}\)

Hint:

Whenever a matrix is singular, immediately use the condition \(|A|=0\). Expanding the determinant often reduces the problem to a simple polynomial equation.

Answer 1

The Correct Option is D