Mathematics - Determinant Question with Solution | TestHub

$∆=\left|\begin{array}{ccc}1& 1& 1\\ 1& 2& 2\\ 1& 3& \lambda \end{array}\right|=\left(\lambda -3\right)$
${∆}_1=\left|\begin{array}{ccc}5& 1& 1\\ 6& 2& 2\\ \mu & 3& \lambda \end{array}\right|=4\left(\lambda -3\right)$
${∆}_3=\left|\begin{array}{ccc}1& 5& 1\\ 1& 6& 2\\ 1& \mu & \lambda \end{array}\right|=\lambda -\mu +4$
${∆}_4=\left|\begin{array}{ccc}1& 1& 5\\ 1& 2& 6\\ 1& 3& \mu \end{array}\right|=\mu -7$
For infinite many solution$∆={∆}_1={∆}_2={∆}_3=0$
$\Rightarrow \lambda =3, \& \mu =7$from$∆=0 \& {∆}_4=0$
&$\lambda =3, \mu =7$Satisfies${∆}_3=0={∆}_1$
$\therefore \lambda +\mu =10$