Consider the set of vectors (columns) defined by X = {x ∈ R3 ∶ x1 + x2 + x3 = 0, where xT = [x1, x2, x3]T}, Which of the following is true?
1
{[1, -1, 0]T, [1, 0, -1]T) is a basis for the subspace X.
2
{[1, -1, 0]T, [1, 0, -1]T) is a linearly independent set, but it does not span X and therefore is not a basis of X.
3
X is not a subspace for R3.
4
None of the above