Linear Map Lemma Independence Corollary

A corrolary from Linear Map Lemma and Linear Independence Extension Lemma

Corrolary

1. For any linearly independent set $\{v_1,\dots ,v_m\}\subset V$ for Vector Space $V$
2. For any subset $\{w_1,\dots ,w_m\}\subset W$, for Vector Space $W$
3. There is a Linear Map $T\in L(V,W)$ s.t $T(v_k)=w_k$