 Solution

The remaining eigenvalue is $\boxed{{\lambda }_3=0}$. At a steady state, the three cyclic fluxes agree: $ϵA=\eta B=\delta C$. A corresponding nonzero eigenvector is thereforeor its scalar multiple $(\delta \eta ,ϵ\delta ,ϵ\eta {)}^T$. Its positive components express a possible equilibrium concentration ratio.