Let V be a vector space over the universal set and S and T be two non-empty finite sets with S $\subset$ T. Show that $<S>$ $\subset$ $<T>$ where denotes the linear span of A.
I did something like this: since S is a subset of T, every element in S can be expressed using the basis of T, but I don't know how we can eliminate some elements from the basis of T to make the basis of S.
Also, it is not possible that their linear spans are the same?
Hint-If $S$ is a subset of $T$ , every vector in $S$ is a vector in $T$. Now $Span(T)$ is , by definition the smallest vector space containing $T$, and $Span(S)$ is the smallest vector space containing $S$ .