Definition:Linear Combination of Subsets of Vector Space/Binary Case

Definition
Let $K$ be a field.

Let $X$ be a vector space over $K$. Let $A$ and $B$ be subsets of $X$ and $\lambda, \mu \in K$.

We define the linear combination $\lambda A + \mu B$ by:


 * $\lambda A + \mu B = \set {\lambda a + \mu b : a \in A, \, b \in B}$