Kernel of Linear Transformation contains Zero Vector

Corollary to Linear Transformation Maps Zero Vector to Zero Vector
Let $\mathbf V$ be a vector space, with zero $\mathbf 0$.

Likewise let $\mathbf V'$ be another vector space, with zero $\mathbf 0'$.

Let $T: \mathbf V \to \mathbf V'$ be a linear transformation.

Then:
 * $\mathbf 0 \in \map \ker T$

where $\map \ker T$ is the kernel of $T$.

Proof
Follows from Linear Transformation Maps Zero Vector to Zero Vector and the definition of kernel.