Question

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

• A. $0$
• B. $6$
• C. $-6$
• D. $-4$
• E. $4$

Answer 1

The correct option is E

$4$

Explanation for the correct option:

To find the value of $5k-k^2$:

Since the matrix is singular

$$\begin{gathered} \Rightarrow \left|A\right|=0 \\ \Rightarrow \left|\begin{array}{cc}2-k& 2\\ 1& 3-k\end{array}\right|=0 \\ \Rightarrow \left(2-k\right)\left(3-k\right)-2=0 \\ \Rightarrow 6-5k+k^2-2=0 \\ \Rightarrow 5k-k^2=4 \end{gathered}$$

Hence, the correct option is (E).