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:
 * $\mathbf 0 \in \ker \left({T}\right)$

where $\ker \left({ T }\right)$ is the kernel of $T$.

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