Math 210-01: Linear Algebra: Reading Homework 4.4

1. Spanning Sets and Linear Independence : what is a linear combination? what do we do with linear combinations in this section?
   
   1. Finding linear combinations : how can we find if a vector can be written as a linear combination of other vectors?
      
   2. Spanning Sets : what is a spanning set of a vector space? what are the standard spanning sets of R² and P₂?
      
      1. finding spanning sets : how can we determine if a set spans a vector space?
         
      2. span of a set : what is the span of a set? how is the span of a set related to subspaces?
         
   3. Linear Dependence and Independence : what is meant when we say that a set is linearly independent? linearly dependent?
      
      1. testing for linear (in)dependence : how can we test if a set of vectors is linearly (in)dependent?
         
      2. linear dependence : what does it mean about vectors in a set if the set is linearly dependent?