Suppose we have a system of $m$ equations in $n$ variables, with coefficient matrix $A$ and vector of constants $\vect{b}$. Then the augmented matrix of the system of equations is the $m\times(n+1)$ matrix whose first $n$ columns are the columns of $A$ and whose last column ($n+1$) is the column vector $\vect{b}$. This matrix will be written as $\augmented{A}{\vect{b}}$.