AP EAMCET · Maths · Determinants
\(A=\left[\begin{array}{ccc}0 & k & k \\ k & -4 & -6 \\ k & -3 & -5\end{array}\right]\) is a singular matrix for
- A \(\mathrm{k}=2\) only
- B \(k= \pm 2\) only
- C no real value of \(k\)
- D all real values of \(k\)
Answer & Solution
Correct Answer
(D) all real values of \(k\)
Step-by-step Solution
Detailed explanation
det(A) = \(0((-4)(-5)-(-6)(-3)) - k(k(-5)-(-6)k) + k(k(-3)-(-4)k) = 0\) \(0(20-18) - k(-5k+6k) + k(-3k+4k) = 0\) \(0(2) - k(k) + k(k) = 0\) \(-k^2 + k^2 = 0\) \(0 = 0\) The matrix is singular for all real values of \(k\).
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