Vector space/Generating system and spanned subspace/Fact/Proof/Exercise

Let ${}K$ be a field, and let ${}V$ be a ${}K$-vector space. Show that the following statements hold.

1. For a family ${}v_{i}$, ${}i\in I$, of elements in ${}V$, linear span is a linear subspace of ${}V$.
2. The family ${}v_{i}$, ${}i\in I$, is a spanning system of ${}V$ if and only if

   ${}\langle v_{i},\,i\in I\rangle =V\,.$

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