The essential information for a system of linear equations may be encoded in a matrix.

Given the system

    a11 x1 + a12 x2 + a13 x3 =  b1
    a21 x1 + a22 x2 + a23 x3 =  b2
    a31 x1 + a32 x2 + a33 x3 =  b3

the coefficient matrix is

a11 a12 a13
a21 a22 a23
a31 a32 a33

and the augmented matrix is obtained by tacking on the constants on the right-hand sides of the equations:

a11 a12 a13 b1
a21 a22 a23 b2
a31 a32 a33 b3