1. The problem statement, all variables and given/known data erm, I just want to know, what is the basis for a zero vector space? 2. Relevant equations 3. The attempt at a solution is it the zero vector itself? but if that's the case, then the constant alpha could be anything other than zero, which means the zero vector is not linearly independent... another quick question, how do you determine the basis of a polynomial vector space in general?