Math 214 Assignment for Unit 7
Due: In class Wednesday March 11, 2015
Your report should include your work for each of these problems. 
Part 7a: Independence, Basis and Dimension.
page 178 (section 3.5):   # 2, 8, 13, 16, 20.

Part 7b:  The Four Subspaces.
page 190 (section 3.6):   # 4, 5, 10, 11, 24, 26, 27.
    Comment:  # 4: For part e) make the argument based on dimensions of the spaces.
                The argument can be made complete once we have orthogonal 
                complements, but use this as an exercise in dimensions.
    Comment:  # 10: Random entries make it hard to get dependent vectors.

Part 7c: Orthogonality of the Four Subspaces
page 202 (section 4.1):   # 3, 7, 9, 13, 16, 19, 24.
    Comment:  # 13: You need to argue that not only the bases are orthogonal 
            but that this means that all vectors in the spaces are orthogonal.
              # 19: Do # 18 before doing this problem (its answer is in the back).
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?