> [!Definition] Definition (Augmented matrix) > Let $\forall i \in \{ 1,2,\dots,m \}: \sum_{j=1}^{n} a_{ij}x_{j}=b_{i}$be a [[Linear System of Equations|linear system of equations]]. Then the augmented matrix of the system is given by $(A\mid \underline{b})$ where $A = \left(\begin{array}{cccc}a_{11} & a_{12} & \cdots & a_{1 n} \\a_{21} & a_{22} & \cdots & a_{2 n} \\\vdots & \vdots & & \vdots \\a_{m 1} & a_{m 2} & \cdots & a_{m n}\end{array}\right),\quad \underline{b}=(b_{1},b_{2},\dots,b_{n})^{T }$