a coefficient matrix for a system of linear equations is the matrix whose (i,j) entry is the jth variable of the ith equation.

An example:
Given the following system of linear equations:
1x + 2y + 3z = 99
2x + 3y + 1z = 33
3x + 1y + 4z = 22

The coefficient matrix would be as follows:

       |1 2 3|
       |2 3 1|
       |3 1 4|

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