Let L: \mathbb{R}^3 \to \mathbb{R}^3 be a linear map defined by L(x, y, z) = (x + 2y, 2x + 3y + z, x + y + z).
Then what is the kernel of L?
a) KerL = \{(0,0,0)\}.
b) KerL = \{(x, y, z) \in \mathbb{R}^3 | x + 2y = 0\}.
c) KerL = \{a(-2,1,1)|a \in \mathbb{R}\}.
d) KerL = \{(0,0,0), (-2,1,1)\}.
e) None of the choices in the list is correct.