In each case, find a basis B = {e1,..., er, er+1,..., en} of V such that {er+1,...,

Question:

In each case, find a basis
B = {e1,..., er, er+1,..., en} of V such that {er+1,..., en) is a basis of ker T, and verily Theorem 5.
(a) T: R3 → R4; T(x, y, z) = (x -y + 2z, x + y - z, 2x + z, 2y - 3z)
(b) T: R3 → R4; T(x, y, z) = (r + y + z, 2x - y + 3z, z - 3y, 3x + 4z)