Necessary and sufficient conditions for the generic solvability of ＇the extended fundamental problem in residual generation＇ (EFPRG) (Massoumnia et al., 1989, IEEE Trans. Automat. Control 34, 316-321) in the case of simultaneous actuator and sensor failures are presented. In the process of deriving these conditions, the generic forms of supremal controllability and infimal unobservability subspaces of LTI systems having diagonal state-space matrices are obtained.