Condensing Timetables with Target Date Divisible by Each Instructor's Number of Teaching Hours

Initial data required to construct a school timetable which can be represented as a matrix with a constant number of nonzero elements in each row and a constant set of elements in each column are considered. Conditions are determined under which this matrix can be transformed so that the sets of elements in each row and each column are preserved and the nonzero elements in every row are consecutive.