Span

A function to create a set from all vectors in $V$ into the set of all linear combinations of those vectors.

Denoted as $span\{\overrightarrow{x_1},\dots ,\overrightarrow{x_k}\}$ or $span(X)=\{a_1{x}_1+a_k\overrightarrow{x_k};a_1\dots a_k\in R\}$

• Span of X is a Subspace itself as its Closed Under Linear Combinations and should have the 0 vector.
• $X\subset span(X)$ (Refer to Subset) You write a span $span(\{(1,0),(0,1)\})$ as $\{x(1,0)+y(0,1):x,y\in R\}$