> [!NOTE] Definition > Let $A\in \text{Mat}_{mn}(\mathbb{R})$ be a [[Real Matrices|real matrix]] of order $m\times n.$ Let $\lambda\in \mathbb{R}.$ Then $\lambda A$ is given by the matrix $C\in \text{Mat}_{mn}(\mathbb{R})$ whose $(i,j)$ entry is given by $c_{ij}=\lambda a_{ij}$for all $(i,j)\in [1,2,\dots,m]\times[1,2,\dots,n].$