On Quasilinear Algebra of Linear Interval Equations and Interval Cramer’s Rule

Determining the solution set of a system of linear interval equations is often a difficult task. Establishing a general theory that includes the classical theory of systems of linear equations as a special case opens the door to extensive and challenging research. In this study, we aim to develop results concerning the solution sets of such systems by employing the concept of quasilinear spaces. First, we define the determinant of an interval matrix as an interval and its rank as a pair of natural numbers. Then, we introduce the concept of a quasi-inverse for interval matrices and derive several results based on this notion. Using these results, we prove a theorem, which we call the interval Cramer’s rule, concerning the solutions of certain linear interval equation systems. In addition, with respect to the existence of solutions for this type of equation, we present a theorem related to the rank of the interval matrix that models the system.