Find a basis for 
for the subspace S.
Definitions:
Extinction
In psychology, the gradual weakening and eventual disappearance of a conditioned response when the conditioned stimulus is no longer paired with an unconditioned stimulus.
Conditioned Fear
A learned response to a stimulus that was previously neutral but has been paired with an aversive event.
Loud Noise
Auditory stimuli that are of high decibel level, potentially causing hearing damage or stress.
Toy Dog
A term used to describe small dog breeds that are often kept as companions or pets, characterized by their compact size and playful nature.
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