there is a property that states

$\displaystyle T:V\rightarrow W$ is a one-to-one linear transformation, and $\displaystyle k={v_1,...,v_s}$ is a set of independent vectors in V. So the image $\displaystyle T(K)={T(v_1),...,T(v_s)}$ is a set of independent vectors in W.

My question is, does that necessarily mean that if $\displaystyle T:V\rightarrow W$ isnota one-to-one linear transformation then the image of those vectors is a set ofdependentvectors.

If so, can someone please show an example against my claim.