# Definition:Linear Combination/Sequence

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## Definition

Let $G$ be an $R$-module.

Let $\left \langle {a_n} \right \rangle := \left \langle {a_j} \right \rangle_{1 \mathop \le j \mathop \le n}$ be a sequence of elements of $G$ of length $n$.

An element $b \in G$ is a linear combination of $\left \langle {a_n} \right \rangle$ if and only if:

$\displaystyle \exists \left \langle {\lambda_n} \right \rangle \subseteq R: b = \sum_{k \mathop = 1}^n \lambda_k a_k$