Which of the following sets is a basis for R3\mathbb{R}^3R3?
{⟨1,0,0⟩,⟨0,1,0⟩}\{\langle 1,0,0 \rangle, \langle 0,1,0 \rangle\}{⟨1,0,0⟩,⟨0,1,0⟩}
{⟨1,1,0⟩,⟨0,1,1⟩,⟨1,0,1⟩}\{\langle 1,1,0 \rangle, \langle 0,1,1 \rangle, \langle 1,0,1 \rangle\}{⟨1,1,0⟩,⟨0,1,1⟩,⟨1,0,1⟩}
{⟨1,0,0⟩,⟨0,1,0⟩,⟨0,0,0⟩}\{\langle 1,0,0 \rangle, \langle 0,1,0 \rangle, \langle 0,0,0 \rangle\}{⟨1,0,0⟩,⟨0,1,0⟩,⟨0,0,0⟩}
{⟨1,2,3⟩,⟨2,4,6⟩,⟨0,0,1⟩}\{\langle 1,2,3 \rangle, \langle 2,4,6 \rangle, \langle 0,0,1 \rangle\}{⟨1,2,3⟩,⟨2,4,6⟩,⟨0,0,1⟩}