An augmented matrix is a formal rectangular array in linear algebra constructed by appending the constant terms vector to the coefficient matrix of a system of linear equations. This structure encodes both variable relationships and solution constraints within a unified tabular representation, facilitating systematic row reduction operations such as Gaussian elimination or Gauss-Jordan normal form. The concept serves as the foundational data structure for algorithmically determining solution spaces, including unique solutions, infinite sets, or inconsistency, within the subfield of matrix theory and linear systems analysis.
Builds the augmented matrix of a linear system by adjoining the constants column to the coefficient matrix.