Q114 / 180 · COMEDK 2023 (Morning Shift) · Mathematics
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
- Correct answerA$\pm 3$
- B$\pm 1$
- C$\pm 4$
- D$\pm 2$
Solution
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 a singular matrix:
$k^2 - 9 = 0$
$k^2 = 9$
$k = \pm 3$
Answer: $\pm 3$
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 a singular matrix:
$k^2 - 9 = 0$
$k^2 = 9$
$k = \pm 3$
Answer: $\pm 3$
Hence, the correct answer is option: 'A'.