Question

For what value of k, the matrix $\left[\begin{array}{cc}2-k& 4\\ -5& 1\end{array}\right]$ is not invertible ?

Answer 1

$A=\left[\begin{array}{cc}2-k& 4\\ -5& 1\end{array}\right]$ is not invertible.

That is, A is singular matrix, then $|A|=0$.

$\left|\begin{array}{cc}2-k& 4\\ -5& 1\end{array}\right|=0$

$2-k+20=0$

$k=22$