Thread: subspace and basis (true false)

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.

Originally Posted by Taurus3

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.

1) What have you done so far?, and

2) What in the world is "rref"?

Tonio

I'm guessing that rref(A) is the reduced echelon form of A.