Final answer:
The capability to take off with one AHRS in BASIC mode largely depends on aviation regulations and the specific requirements for redundancy in commercial operations. It is usually not permitted, but special dispensations can exist under certain conditions.
Step-by-step explanation:
Whether you can take off with one AHRS (Attitude and Heading Reference System) in BASIC mode depends on the regulations of the aviation authority you are operating under, as well as the specific operating procedures of the aircraft and the airline or operator. Generally, for commercial operations, there is a requirement for redundant systems to ensure safety. So, if one AHRS is in basic mode and the other systems are not operational, it may not meet the redundancy requirement. However, in some cases, an aircraft with a single functional AHRS might be able to continue operations under a special dispensation or in a de-rated operational capacity.