$L: \mathbb{R}^2 \to \mathbb{R}^2$ defined by $L(x_1, x_2) = (2x_1 + x_2, -3x_1 + 2x_2)$
Find a basis for Ker($L$)
I solved $$L(x_1, x_2) = 0$$ and the only solution I have is $(x_1, x_2) = (1, 1)$, which is a finite set, so there cant be a basis right?