Determine the set of solutions of the new system depending on the parameter k.Determine the dimension of the space of the solutions and the set of solutions of system S employing Gaussian elimination.

Consider the following linear system S 2w + x + y +z = a w+y+z= b W+y= 2

Determine the dimension of the space of the solutions and the set of solutions of system S employing Gaussian elimination.

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.