## Terminology for Linear Systems

Key terms used when working with linear systems in matrix form:

- **Linear system**: A collection of one or more linear equations involving the same variables
- **Consistent system**: A system that has at least one solution
- **Inconsistent system**: A system that has no solution
- **Homogeneous system**: A system where all constant terms are zero (`Ax = 0`)
- **Non-homogeneous system**: A system where at least one constant term is nonzero
- **Free variable**: A variable that can take any value (corresponds to non-pivot columns)
- **Basic (leading) variable**: A variable corresponding to a pivot column in echelon form
- **Augmented matrix**: The coefficient matrix with the constant vector appended as an extra column
- **Coefficient matrix**: The matrix containing only the coefficients of the variables
- **Row echelon form**: A matrix form where each leading entry is to the right of the one above
- **Reduced row echelon form**: Row echelon form where each pivot is 1 and is the only nonzero entry in its column