Math 2602  B1 , B2                                                                  Homework # 10
                                     Due Tuesday, November 9, 2004

 
                       
  1.  Let  Ax  =  b  be the matrix/vector form of the following linear system:

              2x + 2y + 4z + 4 w = 2
              2x + 2y + 5z + 3w  = 2
              3x + 3y + 7z + 5w  = 3

   (i)  Find all solutions to this system.

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

   (iii) The vector  (1 , -1 , 1 , -1 )^T  is a solution to  Ax = b when b = ( 0 , 2 , 2 )^T .  Find all solutions
          in this case.