3. (10%) Let $T: V \to W$ be a linear transformation and $B = \{\vec{v}_1, \vec{v}_2, \dots, \vec{v}_n\}$ be a spanning set for $V$. Please show that $T(B) = \{T(\vec{v}_1), T(\vec{v}_2), \dots, T(\vec{v}_n)\}$ spans the range of $T$.