Part 4a: Transposes and Permutation
  pg 115 (section 2.7):   # 4, 13, 19, 40.
    Comments:  # 4: You need more than examples to show A^TA=0 not possible.
    Comments:  # 13: This problem uses a symbol P with a hat on it.  That 
       can just be treated as another letter (say Q).  It does not suggest 
       any relationship to P.
    Comments:  # 33: This operation is a rotation of the coordinate axes.
       The problem points out what line it is rotating about.  You can
       answer the question about angle without any algebraic manipulation.

Study for the exam by 
  1) reading the text and lecture notes, 
  2) doing problems from the list of good problems, 
  3) making an outline of the course so far and 
  4) creating example problems of your own for the exam.