Let Ax = b, b ≠ 0, be a consistent linear system.
(a) Show that if xp is a particular solution to the given nonhomogeneous system and xh, is a solution to the associated homogeneous system Ax = 0, then xp + xh, is a solution to the given system Ax = b.
(b) Show that every solution x to the nonhomogeneous linear system Ax = b can be written as xp + xh, where xp is a particular solution to the given nonhomogeneous system and xh, is a solution to the associated homogeneous system Ax = 0.