> [!NOTE] Lemma > Let $n \geq 1.$ Let $\mathbb{R}^{n}$ denote the [[Real n-Space|real n-space]]. Let $\underline{0}$ denote the [[Real Zero Vector|zero vector]]. Let $\underline{v}\in \mathbb{R}.$ Then $0\underline{v}=\underline{0}$where $0\underline{v}$ denotes a [[Scalar Multiplication in Real n-Space|scalar multiple]] of $\underline{v}.$ **Proof**: Follows from definition of scalar multiplication and $\underline{0}.$ # Applications **Generalisation**: See [[Scalar Multiplication by Zero in Real Vector Space]].