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 |