COMEDK · Maths · 22. Determinants
If \(A=\left[\begin{array}{ccc}0 & x & 16 \\ x & 5 & 7 \\ 0 & 9 & x\end{array}\right]\) is a singular matrix then \(x\) is equal to
- A \(-144\)
- B 144
- C 21
- D \(-12\)
Answer & Solution
Correct Answer
(D) \(-12\)
Step-by-step Solution
Detailed explanation
For singular matrix, \(|A| = 0\) Expanding along first column (two zeros): \(|A| = 0 - x\begin{vmatrix} x & 16 \\ 9 & x \end{vmatrix} + 0\) \(= -x(x^2 - 144)\) Setting \(|A| = 0\): \(-x(x^2 - 144) = 0\) \(x = 0\) or \(x = \pm 12\) Among the given options, \(x = -12\).
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