Find all subsets of the set that forms a basis for R2.

Find all subsets of the set that forms a basis for R2.
S = { (1, 0), (0, 1), (1, 1) }

I have no idea how to do this

A basis for R2 must consist of exactly two linearly independent vectors in R2. *Two* vectors are linearly independent precisely when both vectors are nonzero, and the vectors are not scalar multiples of each other.

(1, 0) and (0, 1) are both nonzero and are not scalar multiples of each other.
(1, 0) and (1, 1) are both nonzero and are not scalar multiples of each other.
(0, 1) and (1, 1) are both nonzero and are not scalar multiples of each other.

So the three possible subsets of S that are bases for R2 are
{(1, 0), (0, 1)}, {(1, 0), (1, 1)}, and {(0, 1), (1, 1)}.

Lord bless you today!