Linear Transformations Preserve Additive Identities

If $T:V\to W$ is a linear transformation, then $T(0v)=0w$

Proof

In vector space we have $\hat{0}=\hat{0}\overrightarrow{z}$ for all $\overrightarrow{z}$ Suppose $T:V\to W$ is a Linear Transform $T(\hat{0}\overrightarrow{v})=T(\hat{0}⊡\overrightarrow{v})$