Official solution
\[\begin{aligned}
&\begin{aligned}
& \mathrm{D}=\left|\[\begin{gathered} 1 \quad 2 \quad -3 \\ 2 \quad \lambda \quad 5 \\ 14 \quad 3 \quad \mu \end{gathered}\end{aligned}\end{aligned}\]\right|=0, \lambda \mu+42 \lambda-4 \mu+107=0 \\
\& \mathrm{D}\_1=2 \lambda \mu+99 \lambda-10 \mu+255 \\
\& \mathrm{D}\_2=13-\mu \\
\& D\_3=5 \lambda+5 \\
\& D\_2=0 \Rightarrow \mu=13 \& D\_3=0 \Rightarrow \lambda=-1
\\
\&\text { check \& verify for these values } \mathrm{D} \& \mathrm{D}\_2=0
\]