Algebraic method for independence model of two-way contingency tables

The main purpose of the study is to propose an algebraic method to obtain the set of all independence models of i × j two-way contingency tables with the same row sums and column sums which is called fiber in algebraic statistics. this method involves solving a system of linear algebraic equations that only rely on row sums and column sums of the i × j two-way contingency table. the matlab software was used to solve this system. the effectiveness of the purposed method is illustrated by applying to a contingency table of agriculture teachersperception of secondary school agriculture.