Span

Definition

Let \(S\in V\), \(\text{span}(S)=\) set of all Linear Combination of vectors of \(S\). If \(S=\emptyset\), $\text{span}(S)=\lbrace 0\rbrace $.

Theorem

Let \(S\subset V\) then \(\text{span}(S)\) is a subspace of \(V\). Moreover, if \(W<V\) and \(S\subset W\), then \(\text{span}(S)\subset W\)

HW

Show that \(c\in F\), then \(cx\in \text{span}(S)\)

Show "If \(S=\emptyset\), $\text{span}(S)=\lbrace 0\rbrace $."