solve the following system of equtions and give the general
solution in parametric vector form. 

  x + y - 2z     = 6
     3y +  z - w = 3
-2x + y + 2z - w = 9

Associated with this linear system is the augmented matrix



Reducing it to row reduced echelon form:



So the general solution is 

 = 

Write the -6 as -6+0w, and the w as 0 + 1w

 = 

Write the matrix on the right as the sum of two matrices:

 =  + 

Now factor out a scalar w from the right-hand matrix:

 =  + w

That's fine in that form, however, it looks neater when you factor out
1/3 from the matrix on the right:

 =  + 

Edwin