Linear Combination

Definition: Linear Combination

Let $(V,F,+,\cdot )$ be a vector space

We say that $\mathbf{v}\in V$ is a linear combination of some vectors ${\mathbf{v}}_1,\cdots ,{\mathbf{v}}_n\in V$ iff there exist $c_i\in F$ such that

$$\mathbf{v}=c_1{\mathbf{v}}_1+\cdots +c_n{\mathbf{v}}_n$$