$\begin{aligned}
& \Delta=\left|\begin{array}{ccc}
1 & 2 & -3 \
2 & \lambda & 5 \
14 & 3 & \mu
\end{array}\right|=0 \Rightarrow \lambda \mu+42 \lambda-4 \mu+107=0 \
& \Delta_1=\left|\begin{array}{ccc}
2 & 2 & -3 \
5 & \lambda & 5 \
33 & 3 & \mu
\end{array}\right|=0 \Rightarrow 2 \lambda \mu+99 \lambda-10 \mu+255=0 \
& \Delta_2=\left|\begin{array}{ccc}
1 & 2 & -3 \
2 & 5 & 5 \
14 & 33 & \mu
\end{array}\right|=0 \Rightarrow \mu=13
\end{aligned}Also,\lambda=-1Hence,\lambda+\mu=13-1=12$