Math 2602 B1, B2                                                                                       Homework  #9

                                            Due Thursday, November 6, 2003

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

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

   (i)  Find all solutions for 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 , 0 )^T is a solution to Ax = b , where b = ( 4 , 0 , 2 )^T .
          Find all solutions to this system.