Use Maple's LinearSolve routine (or other equivalent software) to solve the system of equations:
◦ (x, y, z, u, v) = (1 + t, 1 + t, 2 - t, 2 - t, t) for any real number t
◦ (x, y, z, u, v) = (1 + t, 1 - t, 2 + t, 2 - t, t) for any real number t
◦ (x, y, z, u, v) = (2 + t, 1 - t, 2 + t, 1 - t, t) for any real number t
◦ (x, y, z, u, v) = (1 + t, 1 + t, 2 + t, 2 - t, 3t) for any real number t
◦ (x, y, z, u, v) = (1 + t, 1 - t, 2 +t, 2 - t, 0) for any real number t