**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`.