The first system element that responds quantitatively to the measured variable and performs the initial measurement operation is a ------

The correct choice is the detector, as it serves as the initial point in a measurement system where the physical variable is sensed and converted into a measurable signal. Detectors are designed to capture data from various physical phenomena, such as temperature, pressure, or flow, and provide a quantitative representation of those variables.

In the context of instrumentation, the detector is crucial as it directly interacts with the measured environment and produces an output that can be further processed by other components of the system, such as transmitters or controllers. Understanding this foundational role of the detector is critical in grasping the overall functionality of measurement systems in instrumentation.