Part 1a: Vectors and Matrices    
page 8  (section 1.1):   # 5, 16, 30.
    Comment:  # 5: Use words (complete sentences) to answer the second part. 
              # 16: Read #15 first. Graphically show it is a line.  
               You can write the line algebraically as vectors v + d(w-v) for all scalars d.  
page 19 (section 1.2):   # 19, 28.
page 29 (section 1.3):   # 4, 5, 14.

Part 1b: Systems of Linear Equations
page 40 (section 2.1):   # 5, 7, 12, 19, 33.
    Comments:  # 7: Definition:  A matrix is singular if there are not enough pivots during elimination.
                    This also means that its columns are dependent.
            Answers in the book for #12 are really for #11.
               # 19: The question uses the name E^-1 for a second matrix.  Just treat that as another 
               name like F.  It will turn out to be the inverse of E but we don't need that notation here. 
page 51 (section 2.2):   # 4, 5, 7, 8, 11, 12, 14, 20, 25.
    Comments:   #20: When creating the third equation make sure it is not parallel to another.
                 Choose the third equation such that the third row of A is a linear combination 
                 of the first two rows.  Note that this makes sure no two planes are parallel.

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?