Definition
Let linear system of equations in unknowns:
a_{11}x_{1} & + & a_{12}x_{2} & + & \dots & + & a_{1n}x_{n} & = & b_{1} \\ a_{21}x_{1} & + & a_{22}x_{2} & + & \dots & + & a_{2n}x_{n} & = & b_{2} \\ \vdots & & \vdots & && & \vdots & & \vdots \\ a_{m1}x_{1} & + & a_{m2}x_{2} & + & \dots & + & a_{mn}x_{n} & = & b_{m} \\ \end{matrix} $$ Then the **augmented [[3 Reference/Def-matrix\|matrix]]** of the linear system is written as\begin{bmatrix} a_{11} & a_{12} & \dots & a_{1n} & b_{1} \ a_{21} & a_{22} & \dots & a_{2n} & b_{2} \ \vdots & \vdots & \ddots & \vdots & \vdots \ a_{m1} & a_{m2} & \dots & a_{mn} & b_{m} \end{bmatrix}
## Related theorems - [[3 Reference/1.1 Introduction to Systems of Linear Equations#theorem-elementary-row-operations|Theorem Elementary row operations]]