Let \(V\) be a vector space over a field \(F\). Consider a set of finitely many vectors \(A:=\{x_1,\ldots,x_n|~v_i\in V\}\). The set of all possible linear combinations of the vectors in \(A\) is called the linear span (or the linear hull) of \(A\) and denoted by \(Span(A)\):
\[Span(A):=\{\alpha_1 x_1 + \ldots \alpha_n x_n|~\alpha_i\in F,~x_i\in A\}\]
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