Math 214 Assignment for Unit 5
Due: In class Wednesday February 25, 2015
Your report should include your work for each of these problems.
Part 5a: Vector Spaces
page 127 (section 3.1):   # 4, 10, 15, 17, 25, 28.
    Comment:  # 10: Follow the instructions for Q9-18... Show whether x+y and cx are in the subset
                for arbitrary vectors x, y, and scalar c.  Often the hard part is writing x in an 
                arbitrary way.
              # 10: (b1,b2,b3) is a 3x1 vector with entries b1, b2 and b3.  (The bs are not vectors.)
              # 10: To show it IS a subspace requires arbitrary x.  To show it is NOT a subspace 
              requires only one example where either x+y or cx is not in the subset.
              # 17, see section 2.5 #11.

Part 5b: Null Space of A
page 140 (section 3.2):   # 1, 2, 3, 9, 13.

Executive Summary: You are required to answer each question with complete sentences.
  1. What idea do you believe is the most important in each part and why?
  2. What troubles did you have with the assignment, if any?