Augmented matrix
A coefficient matrix with one
a supplementary column vector containing all constants
of the associated linear system
\begin{equation*} \begin{cases} a_{11} x_1 + a_{12} x_2 + a_{13} x_3 + \cdots + a_{1n} x_n = b_1 \\ a_{21} x_1 + a_{22} x_2 + a_{23} x_3 + \cdots + a_{2n} x_n = b_2 \\ a_{31} x_1 + a_{32} x_2 + a_{33} x_3 + \cdots + a_{3n} x_n = b_3 \\ \vdots \\ a_{m1} x_1 + a_{m2} x_2 + a_{m3} x_3 + \cdots + a_{mn} x_n = b_m, \end{cases} \end{equation*}in the form
\begin{equation*} \begin{pmatrix} a_{11} & a_{12} & a_{13} & \cdots & a_{1n} & b_1 \\ a_{21} & a_{22} & a_{23} & \cdots & a_{2n} & b_2 \\ \vdots & \vdots & \vdots & \ddots & \vdots & \vdots \\ a_{m1} & a_{m2} & a_{m3} & \cdots & a_{mn} & b_1 \end{pmatrix}. \end{equation*}