augmented matrix

A system's coefficients and constants compressed into one grid.

For a system of $m$ linear equations in $x_1,\dots,x_n$ , the coefficient matrix $A$ is the $m\times n$ array of coefficients, and the augmented matrix appends one more column — the right-hand-side constants — to the right of $A$ . Row $i$ of the augmented matrix is equation $i$ : its entries are the coefficients of $x_1,\dots,x_n$ followed by the constant $b_i$ , and nothing else.