This book is designed for wide use in colleges and universities by beginners and more advanced students in studying of Linear Algebra and Programming .Its features and considered methods in general concern to evaluation of matrix determinant by Laplace's and Expansion methods with use of functional graphs and includes the following aspects: The general principles of Laplace's and Expansion methods Functional graphs and algorithms for Laplace's method in process of evaluation of matrix determinant for the different rows and columns(on base of 4∙4 and 5∙5 matrices) Functional graphs and algorithms for Expansion method in process of evaluation of matrix determinant for the different rows and columns (on base of 4∙4 and 5∙5 matrices) Evaluation of some main properties of matrix determinant in examples Practical numerical data for above-considered conditions with solving of multiply linear equations