Determine if the set S={⟨1,0⟩,⟨0,1⟩,⟨1,1⟩}S = \{\langle 1, 0 \rangle, \langle 0, 1 \rangle, \langle 1, 1 \rangle\}S={⟨1,0⟩,⟨0,1⟩,⟨1,1⟩} is a basis for R2\mathbb{R}^2R2.
Yes, it spans R2\mathbb{R}^2R2 and is linearly independent.
No, it is linearly dependent.
No, it does not span R2\mathbb{R}^2R2.
Yes, it is the standard basis.