Determine the kernel of the linear transformation T:R2→R2T: \mathbb{R}^2 \to \mathbb{R}^2T:R2→R2 defined by T(x,y)=(x−y,2x−2y)T(x, y) = (x - y, 2x - 2y)T(x,y)=(x−y,2x−2y).
{(x,x):x∈R}\{(x, x) : x \in \mathbb{R}\}{(x,x):x∈R}
{(0,0)}\{(0, 0)\}{(0,0)}
{(x,−x):x∈R}\{(x, -x) : x \in \mathbb{R}\}{(x,−x):x∈R}
{(1,1)}\{(1, 1)\}{(1,1)}