Linear transformation and dependence of vectors I couldn't find an example or explanation why the following sentence is correct 
If a Transformation is linear, and vectors $u_1$,$u_2$,$u_3$ are dependent then 
$T(u_1)$,$T(u_2)$,$T(u_3)$
must also be dependent 
but
If a Transformation is linear, and $T(u_1)$,$T(u_2)$,$T(u_3)$ are dependent , that doesn't mean vectors $u_1$,$u_2$,$u_3$ are dependent 
Couldn't think of an example that would justify the 2nd phrase 

Let $T$ be the null function and take any $3$ linear independent vectors $u_1$, $u_2$, and $u_3$. Then $\bigl\{T(u_1),T(u_2),T(u_3)\bigr\}$ is linearly dependent (since it is equal to $\{0\}$).
