Terminology
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