For Exercises 2 through 6, prove that T is a linear transformation, and find bases for both N(T) and R(T). Then compute the nullity and rank of T, and verify the dimension theorem. Finally, use the appropriate theorems in this section to determine whether T is one-to-one or onto. 2. T: R3 - R? defined by T(a1, a2, a3) = (a1 - a2, 2a3). %3! 3. T: R2 - R3 defined by T(a1, a2) = (a1 + a2, 0, 2a1 - a2). %3D