\begin{definition}[Definition:Simultaneous Linear Equations/Matrix Representation/Matrix of Coefficients]
Consider the '''system of simultaneous linear equations''' can be expressed as:
:$\ds \forall i \in \set {1, 2, \ldots, m} : \sum_{j \mathop = 1}^n \alpha_{i j} x_j = \beta_i$
expressed in matrix representation as:
:$\mathbf A \mathbf x = \mathbf b$
The matrix $\mathbf A$ is known as the '''matrix of coeffficients''' of the system.
\end{definition}