Math 2602 A1 - A3                                                                                       Homework  #8
                                                  Due Thursday, March 25, 2004

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

                                2x + 6y - 2z + 4w = 0
                                2x + 2y + 2z + 2w = 6
                                3x + 5y + 1z + 4w = 6


   i) Find all solutions of this system.














   ii) Find the dimension of the null space of  A  (i.e., the dimension of the subspace of all solutions
        of  Ax = 0 ).





  iii)  Find a basis for the null space of  A .








   iv)  With the same  A  as above  ( 1 , 1 , 0 , -1 )^T  is a solution of  AX = b , where  b = ( 4 , 2 , 4 )^T .
          Find all solutions to this system.