Mathematics - Determinant Question with Solution | TestHub

$∆=\left|\begin{array}{ccc}\lambda & 2& 2\\ 2\lambda & 3& 5\\ 4& \lambda & 6\end{array}\right|=\lambda \left(18-5\lambda \right)-2\left(12\lambda -20\right)+2\left(2{\lambda }^2-12\right)=-{\lambda }^2-6\lambda +16=\left(\lambda +8\right)\left(2-\lambda \right)$
$∆=0$ for $\lambda =2$,
${∆}_1=\left|\begin{array}{ccc}5& 2& 2\\ 8& 3& 5\\ 10& 2& 6\end{array}\right|$

${∆}_1=5\left[18-10\right]-2\left[48-50\right]+2\left[16-30\right]$

${∆}_1=40+4-28\ne 0$
No solution for $\lambda =2$.