Math 210-01: Linear Algebra: Reading Homework 4.2

1. Vector Spaces : how do we define a vector space? what do we call elements in this set? what proofs are necessary in the definition of a vector space?
   
   1. Definition : how is a vector space defined---in particular, what entities must be in the space, and what axioms must hold?
      
      1. example 2 : is Rⁿ a vector space?
         
      2. example 3 : how does the book show that the set of all 2x3 matrices is a vector space?
         
      3. examples 4 and 5 : what is P_n? what is C(-infinity,infinity)? what are the operations on these?
         
   2. Properties of vector spaces : what restriction do we face when proving properties of vector spaces?
      
      1. showing sets are vector spaces : what do we need to do to show that a set is not a vector space?