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In general, the complexity of phenomena in sciences makes researchers feel obligated to face problems where multiple variables and big volumes of information are presented. Those problems require advanced in order to decipher the concepts and tools for its treatment. For this reason, multivariate techniques were developed long ago, but only the computer evolution and several software packages have caused the power of the multivariate statistics to become important. The problem of the displacement of people from the countryside to cities is a reason for consolidating the concepts and the principal component application technique (PCA). This article explains PCA technique while prefacing the applyed multivariate analysis. In order to study ACP, one first needs the fundamentals of matrix algebra concepts. When developed and then applied in a specific simulation, there is a way to carry and practice the theory related to the technique treated in this article. On the other hand, the simulation development using this technique needs to use other concepts associated with PCA which are explained and interpreted from the analysis of results obtained in the different processes. The analysis of this article points to one conclusion. In spite of the government taking a role for the displaced persons well-being, there is an absence of major efforts that leads to these problematic solutions. [ABSTRACT FROM AUTHOR]