> [!NOTE] Definition (Spanning Set of $\mathbb{R}^{n}$) > Let $\mathbb{R}^{n}$ be a [[Real n-Space|real n-space]]. A spanning set of $\mathbb{R}^{n}$ is a [[Subsets|subset]] $S\subset \mathbb{R}^{n}$ whose [[Span of Subset of Real n-Space|span]] satisfies $\langle S\rangle =\mathbb{R}^{n}.$ # Properties By [[Spanning Set of Real n-Space contains at Least n Elements]], ...