Problem 5: (2 points each) Show that the following transformations are linear. (a) T:R3→R2, where T(x,y,z)=(x+z,−2y). (b) T:R3→R4, where T(x,y,z)=(2x−z,y+z,0,x−3y). (c) T:P2→P3, where T[p(x)]=xp(x). Problem 6: (2 points each) Show that the following transformations are not linear. (a) T(x,y,z)=(x−y,y+z2). (b) T(x,y,z)=(x−y,y+z,1+z)