Question

If $A=\left[\begin{array}{cc}2-k& 2\\ 1& 3-k\end{array}\right]$ is a singular matrix, then the value of $5k-k^2$ is equal to

• A. 0
• B. 6
• C. -6
• D. -4
• E. 4

Answer 1

The correct option is E 4

Given, $A=\left[\begin{array}{cc}2-k& 2\\ 1& 3-k\end{array}\right]$

Also given $A$ is singular.

$\Rightarrow \left|A\right|=0$

Thus $\left|\begin{array}{cc}2-k& 2\\ 1& 3-k\end{array}\right|=0(2-k)(3-k)-2=0$

$\Rightarrow 6-2k-3k+k^2-2=0\Rightarrow k^2-5k+4=0\Rightarrow k^2-5k=-4\Rightarrow 5k-k^2=4$

So, option E is correct.