Learn Russian: Каждая организация должна представлять собой целую систему. - Every organization must represent a whole system.

The phrase представлять собой is a formal way to say 'to be' or 'to constitute'. Literally, it translates to 'to present by means of oneself'. The word собой is the instrumental case of the reflexive pronoun себя.

Why is целую систему in the accusative case instead of the instrumental case?

While other formal verbs of being like являться take the instrumental case for the definition, представлять собой grammatically acts like a standard transitive verb. It requires the accusative case because the organization is literally 'presenting' a whole system as a direct object. That is why we see the feminine accusative endings in целую систему.

Why must we use the imperfective verb представлять here instead of the perfective представить?

When used to mean 'to be' or 'to constitute', this phrase is strictly imperfective because it describes an ongoing, permanent state rather than a completed action. If you used the perfective представить, the meaning would change entirely to something like 'to imagine' or 'to introduce'.

Why is должна used instead of должен or должно?