5. (7 points) Consider the following linear system S 2w + x + y +z = a w+y+z= b W+y= 2

(a) (3 points) Determine the dimension of the space of the solutions and the set of solutions of system S employing Gaussian elimination.

(b) (4 points) Assume that a fourth equation w + ky 1, where k is a real parameter, is added to the system. Determine the set of solutions of the new system depending on the parameter k.