\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(E\) be a \(\mathbb{K}\)-vector space generated by \(7\) vectors. Show that:
  1. any family of \(8\) vectors of \(E\) is dependent;
  2. if a free family of \(E\) has cardinal \(7\), then it is a basis of \(E\).

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