Prove linear dependence Let $S =\{v_1,...,v_k\}$ be a subset of $T=\{v_1,...,v_m\}$. show if $S$ is linearly dependent then $T$ is linearly dependent.


I know to show that something is linearly dependent you should be able to express at least one vector as a linear combination of the others. 
I don't know how to prove this though.
My thought are if I prove $S$ is linearly dependent then I can say that since each vector in $S$ is also in $T$ means that $T$ is also linearly dependent.
If $S$ is a linearly dependent set, and $S$ is a subset of $T$, then $T$ is linearly dependent. If a vector in $S$ can be represented by a linear combination of other vectors in $S$, then that same vector can be represented by the same linear combination in $T$.
Let's call $s_n$ an ordinary vector of $S$. If $s_n$ can be written as a linear combination of, for example, $s_k$ and $s_p$ (also vectors of $S$), then there is linear dependence in $S$, as stated. Note now that $s_n,s_k$ and $s_p$ also belong to $T$, since $S$ is a subset of $T$. Therefore, there is linear dependence in $T$.