the matrix formed by using the coefficient matrix and adding an extra column on the right which contains the constants that each equation in the system is equal to. For example, Given the following system of linear equations:

1x + 2y + 4z = 5
1x + 1y + 1z = 3
2x + 1y + 7z = 4

The aumented matrix looks like this:

|1 2 4 5|
|1 1 1 3|
|2 1 7 4|

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