Definition (Linear combination)

If we have vectors $v_1,...,v_k$ in a vector space $V$, then any vector of the form $$\begin{align*}a_1v_1+...+a_kv_k,\text{ where } a_i\in \mathbb{F}, i=1,...,k\end{align*}$$ is called a Linear Combination of $v_1,...,v_k$.