Question

Find the of $\lambda$, so that the matrix $\left[\begin{array}{cc}5-\lambda & \lambda +1\\ 2& 4\end{array}\right]$ may be singular.

Answer 1

We know that determinant of singular matrix is $0$

So, $\left|\begin{array}{cc}5-\lambda & \lambda +1\\ 2& 4\end{array}\right|$ $=0$

By expanding

$4(5-\lambda )-2(\lambda +1)$$=0$

$(20-4\lambda )-(2\lambda +2)$$=0$

$20-4\lambda -2\lambda -2$$=0$

$6\lambda$$=18$

$\lambda$$=3$