TOPIC: Weak matrix or functional?

You are a project co-ordinator. The project managers have almost no power in this organization. the role of project managers is performed by project coordinators. you find it very difficult to get commitment from resources, as they dont report to you directly. what type of organization you work for?

functional or weak matrix?

I am more inclined for functional ..but the answer said weak matrix as project coordinator's exist in weak matrix organization. According to RITA it can be in both. so which is right?

Answer should be weak matrix only.. Funcational , PM/PC has no power at all and in thsi case he has little power

Can moderators please explain this as well?
Or are we saying Project expeditors can exist in functional, while project co ordinators in weak matrix? They can exist in both?

Weak Matrix = PM has "weak" authority
Functional = Silo-ed departments with each having a functional manager