Math 2602  A1 - A3                                                                                 Homework  #10
                                               Due Tuesday, November 15, 2005


     Let  Ax = b be the matix/vector form of the following linear system:

            4x - 4y + z                = 3
            5x - 5y + z + u + 2v = 5
            2x - 2y        +u + 2v = 2
            2x - 2y + z +u + 2v = 5

      a)  Find all solutions to this system, and express them in vector form.

      b)  Find a basis for the null space of  A (the subspace of all solutions to  Ax = 0)

      c)  Find all solutions (if there are any) in which x = 1 and
 
           i) y = 2 .

           ii) z = 2 .

           iii) u = 2 .

           iv) v = 2 .