Matrix of Coefficients

A linear system’s matrix of coefficients is a matrix that contains only the coefficients of the variables from the equations in the system. It excludes the constants on the right-hand side of the equations.

For example, consider the following linear system:

$$\{\begin{array}{l}{x}_1+x_2-2x_3=22x_1-3x_2+2x_3=4x_1-x_2+x_3=-1\end{array}$$

The matrix of coefficients for this system is:

$$A_c=\left[\begin{array}{ccc}1& 1& -2\\ 2& -3& 2\\ 1& -1& 1\end{array}\right]$$