Definition of coefficient matrix of a linear system

Definition: Coefficient Matrix

The coefficient matrix of a linear system is the m × n matrix containing only the coefficients of the variables, without the constant terms.

For the system:

a₁₁x₁ + a₁₂x₂ + ... + a₁ₙxₙ = b₁
a₂₁x₁ + a₂₂x₂ + ... + a₂ₙxₙ = b₂
...
aₘ₁x₁ + aₘ₂x₂ + ... + aₘₙxₙ = bₘ

The coefficient matrix A is:

A = [a₁₁ a₁₂ ... a₁ₙ]
    [a₂₁ a₂₂ ... a₂ₙ]
    [...  ...  ... ...]
    [aₘ₁ aₘ₂ ... aₘₙ]

Each row corresponds to one equation, and each column corresponds to one variable. The coefficient matrix is denoted A in the standard form Ax = b.