د.اسماء محمد كنان2024-11-272024-11-27https://dspace.academy.edu.ly/handle/123456789/400The Drazin inverse is one of the important topics in linear algebra. It is a necessary tool for studying many applied scientific topics such as physics, chemistry, economics, and others. Sometimes the linear algebraic systems consist of many variables that will need to be used in programming computer to solve it. At the end of 1979, the singularAbstract The Drazin inverse is an important mathematical tool in many fields such that: linear algebra, cryptography, differential equations and engineering. In this thesis, we studied one of the generalized inverses, it is the Drazin inverse of square singular matrices: its definition, properties and its computation. Also we gave the classical Cramer's rule for solving the non-singular square linear algebraic systems, and extend it into a new generalized Cramer's rule. To do that, we computed a new representation for the Drazin inverse depending on the rank of matrix and based on the adjoint matrix. Then we used this representation to obtain a new generalized Cramer's rule. Finally, we used a new generalized Cramer's rule to solve the singular square linear algebraic systems. We gave examples to illustrate our studyThe Drazin Inverse And Generalized Cramer's Rule For Solving Singular Linear Algebraic Systems