>no. your "reason" is essentially just that some total moron might >threaten to punish you unless you memorize the definitions. you could >as easily use such a "reason" to justify any arbitrarily stupid >behavior.
Not arbitrary or stupid.
>|The first question in the exam is likely to be something >|like the following: >| >|1. Give the definition of a vector space. >| >|Or perhaps >| >|2. Let X be .... >|Prove that X is a vector space.
It is certainly reasonable for a linear algebra exam to have a student show that a certain structure is a vector space!