Linear Transformations Closed Under Linear Combinations

Theorem

• $V,W$ be vector spaces
• $S:V\to W$ be a Linear Map
• $T:V\to W$ be a Linear Map
• Any linear combination of $S$, $T$ is also a Linear Map from $V\to W$ ($\forall a,b\in \mathbb{F},aS+bT:V\to W$)