Linear combination - Aetherwisp

A linear combination of a set of elements is the sum of all elements, each multiplied by some coefficient. In the context of linear algebra, given a Vector space $V$ over a field $K$ , the linear combination of the vectors $v_{1},\ldots,v_{n}\in V$ and the scalars $\alpha_{1},\ldots,\alpha_{n}\in K$ is

\alpha_{1}v_{1}+\ldots+\alpha_{n}v_{n}