[Math] Linear Transformation of Dependent set.

Question

Let $V$ and $W$ be vector spaces and let $T: V\to W$ be a linear transformation. Let $\{v_1, v_2,\ldots, v_p\}$ be a linearly dependent set of vectors in $V$. Show that $\{Tv_1, Tv_2,\ldots, Tv_p\}$ is also linearly dependent.

Answer 1

Prove that if $T(v_1),\ldots,T(v_p)$ are linearly independent, then so are $v_1,\ldots,v_p$.