Augmented and Coefficient Matrices

An Augmented Matrix is a matrix derived from the coefficients and constant terms of a system of linear equations, while a Coefficient Matrix is a matrix containing only the coefficients of the system.

Here is an example:

     System                                Augmented Matrix           Coefficient Matrix

5x - 9y + 2z = 5                           [ 5    -9    2   5 ]                  [ 5   -9   2 ]

3x + 7y - 2z = 9                           [ 3     7   -2   9 ]                  [ 3    7  -2 ]

x            + 9z = 20                       [1      0    9  20]                  [ 1    0    9 ]

In the example, the Augmented Matrix have both the coefficients and their constant terms as entries, while the coefficient matrix only have the coefficients.