Let x1 and x2 be solutions to the homogeneous linear system Ax = 0.
(a) Show that x1 + x2 is a solution.
(b) Show that x1 - x2 is a solution.
(c) For any scalar r, show that rx1 is a solution.
(d) For any scalar r and s, show that rx1 + sx2 is a solution.