Augmented Matrix of Coefficients

The augmented matrix of coefficients defines a linear system by coming the matrix of coefficients with the constant vector or solutions from the right hand side of the equation $\vec{b}$.

For example, consider the following linear system:

$$\{\begin{array}{l}{x}_1+x_2-2x_3=2\\ 2x_1-3x_2+2x_3=4\\ x_1-x_2+x_3=-1\end{array}$$

The augmented matrix of coefficients for this system is:

$$\left[\begin{array}{ccccc}1& 1& -2& |& 2\\ 2& -3& 2& |& 4\\ 1& -1& 1& |& -1\end{array}\right]$$

The vertical line is optional and only for visual clarify.