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.

Mathematics

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

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

(b) 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.

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