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|
| 
