Which of the following sets of vectors forms a basis for R2\mathbb{R}^2R2?
{(1,1),(1,−1)}\{(1, 1), (1, -1)\}{(1,1),(1,−1)}
{(0,0),(1,0)}\{(0, 0), (1, 0)\}{(0,0),(1,0)}
{(1,0),(0,1),(1,1)}\{(1, 0), (0, 1), (1, 1)\}{(1,0),(0,1),(1,1)}
{(1,2),(2,4)}\{(1, 2), (2, 4)\}{(1,2),(2,4)}