Explain the concept of priority inversion and why it can be problematic in systems with tasks of different priorities.

Priority inversion is a situation in task scheduler systems where a high-priority task is blocked by a low-priority task because the low-priority task holds a resource (e.g., a mutex) needed by the high-priority task.

The problem occurs when a medium-priority task, not related to the resource, starts executing and occupies the processor, preventing the low-priority task from releasing the resource. As a result, the high-priority task has to wait, even though it should logically have precedence.

This can lead to delays and violations of timing constraints, which is critical in real-time systems. To address this, priority inheritance protocols are used, where the low-priority task temporarily inherits the priority of the task it is blocking to release the resource more quickly.