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 such a theory, which should include the theory of classical systems of linear equations in a special case, opens the door to a very comprehensive and arduous work. In this study, we tried to develop information about the solution sets of such equation systems by using the known quasilinear space concept. First of all, we defined the determinant of an interval matrix as an interval and its rank as a pair of natural numbers. Then, we introduced the quasi-inverse concept for interval matrices and obtained some results based on this. With the help of our results, we proved a theorem that we call the Interval-Cramer's rule regarding the solution of some linear interval equation systems. In addition, regarding the existence of solutions to this type of equations, we give a theorem regarding the rank of the interval matrix that models the equation.