COMEDK · Maths · 22. Determinants
If \(A=\left[\begin{array}{cc}k+1 & 2 \\ 4 & k-1\end{array}\right]\) is a singular matrix, then possible values of \(\mathrm{k}\) are
- A \(\pm 3\)
- B \(\pm 1\)
- C \(\pm 4\)
- D \(\pm 2\)
Answer & Solution
Correct Answer
(A) \(\pm 3\)
Step-by-step Solution
Detailed explanation
A matrix \(A\) is singular if its determinant is zero, i.e., \(|A| = 0\). Given \(A = \begin{bmatrix} k+1 & 2 \\ 4 & k-1 \end{bmatrix}\), the determinant is calculated as: \(|A| = (k+1)(k-1) - (2)(4)\) \(|A| = (k^2 - 1) - 8\) \(|A| = k^2 - 9\) Setting the determinant to zero for…
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