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