Determine which sets of vectors are linearly independent in R3\mathbb{R}^3R3.
{(1,2,−1),(2,4,−2),(3,6,−3)}\{(1, 2, -1), (2, 4, -2), (3, 6, -3)\}{(1,2,−1),(2,4,−2),(3,6,−3)}
{(1,0,1),(0,1,−1),(1,1,0)}\{(1, 0, 1), (0, 1, -1), (1, 1, 0)\}{(1,0,1),(0,1,−1),(1,1,0)}
{(1,1,2),(0,1,1),(−1,0,−1)}\{(1, 1, 2), (0, 1, 1), (-1, 0, -1)\}{(1,1,2),(0,1,1),(−1,0,−1)}
{(2,−1,1),(1,0,1),(0,1,1)}\{(2, -1, 1), (1, 0, 1), (0, 1, 1)\}{(2,−1,1),(1,0,1),(0,1,1)}