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|