Q76 / 180 · COMEDK 2023 (Memory Based) · 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

  • A
    $\pm 1$
  • B
    $\pm 2$
  • Correct answer
    C
    $\pm 3$
  • D
    $\pm 4$

Solution

Given, $A=\left[\begin{array}{cc}k+1 & 2 \\ 4 & k-1\end{array}\right]$ is a singular matrix. $\begin{aligned} & \therefore \quad|A|=0 \\ & \Rightarrow \quad\left|\begin{array}{cc} k+1 & 2 \\ 4 & k-1 \end{array}\right|=0 \\ & \Rightarrow(k+1)(k-1)-4 \times 2=0 \\ & \Rightarrow \quad k^2-1-8=0 \\ & \Rightarrow \quad k^2-9=0 \\ & \Rightarrow \quad k^2=9 \\ & \Rightarrow \quad k= \pm 3 \\ & \end{aligned}$

Hence, the correct answer is option: 'C'.

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