Definition of constant vector of a linear system

Definition: Constant Vector

The constant vector of a linear system is the m × 1 column vector containing the right-hand side values (the constants) from each equation.

For the system Ax = b, the constant vector b is:

b = [b₁]
    [b₂]
    [...]
    [bₘ]

Example: For the system:

2x + y - z = 8
-3x - y + 2z = -11
-2x + y + 2z = -3

The constant vector is:

b = [ 8]
    [-11]
    [ -3]

The constant vector determines whether the system is homogeneous (b = 0) or non-homogeneous (b ≠ 0).