Mathematics - Determinant Question with Solution | TestHub

For non-trivial solution

$\left|\begin{array}{ccc}4& \lambda & 2\\ 2& -1& 1\\ \mu & 2& 3\end{array}\right|=0$

$\Rightarrow -20-6\lambda +\lambda \mu +8+2\mu =0$

$\Rightarrow 2\mu -6\lambda +\lambda \mu =12$

when $\mu =6, 12-6\lambda +6\lambda =12$

which is satisfied by all $\lambda$

When $\lambda =2, 4\mu =24$

When $\lambda =3, 5\mu =30$

When $\mu =-6, -12-6\lambda -6\lambda =12$