Determine whether the following two are true or false. If true, explain why. If false, give a counter example.
1. Let A be and m x n matrix and let R = rref(A). Then if S = {v_1,....v_2} is a basis for N(R), then S is a basis for N(A).
2. If {v_1, v_2, v_3} is a basis for a subspace V of Rn, then {2v_1-2v_2, v_1+v_2+2v_3, v_1+v_3} is also a basis for V.