A formal security model used in computer systems that characterizes the rights of each user with respect to every object in the system is known as a(n) ____________.

The correct answer is the access control matrix. This model is fundamental in computer security as it provides a structured way to define and visualize the permissions granted to users for various objects within a system. Each entry in the matrix represents the relationship between a subject (e.g., a user or a process) and an object (e.g., a file or resource). This allows administrators to clearly specify which users have permission to perform certain actions on specific objects.

By characterizing the rights of each user, the access control matrix helps in enforcing the principles of least privilege and separation of duties, which are critical in reducing the risk of unauthorized access. The matrix can be utilized to ensure that users only have access to the resources necessary for their roles, enhancing overall system security.

In contrast, the other choices present different concepts that do not directly pertain to defining user rights across system objects. Role hierarchy deals with the organization of roles but does not characterize rights in relation to all objects. A hash table is a data structure used for fast data retrieval, and API, or Application Programming Interface, defines how software components should interact, but neither addresses the user-object rights specification directly.