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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?

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    $\begingroup$ Write down the definition of a linear span, and the definition of inclusion, then apply the assumption to these definitions. $\endgroup$
    – Asaf Karagila
    May 28, 2020 at 10:28
  • $\begingroup$ @AsafKaragila I'm not able to understand how to go about it. $\endgroup$ May 28, 2020 at 10:31
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    $\begingroup$ See some general advice: karagila.org/2015/how-to-solve-your-problems $\endgroup$
    – Asaf Karagila
    May 28, 2020 at 10:31

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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 $S$ .

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