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