خيارات التسجيل
Overview
Mathematics 2 is an introductory course in Linear Algebra designed for first-year LMD students in Economics, Commerce, and Management Sciences. This module provides the fundamental mathematical tools necessary for understanding and solving problems involving systems of linear equations, matrix algebra, and transformations.
Linear Algebra is essential not only for advanced mathematics but also for various applications in economics (input-output models), management (optimization problems), computer science (graphics and data analysis), and statistics (regression analysis).
Chapter Summary
This module is organized into four main chapters:
Chapter 1: Matrices and Matrix Operations
This chapter introduces the basic concepts of matrices, including:
- Definition and types of matrices (square, rectangular, row, column, zero, identity, diagonal, symmetric, skew-symmetric, triangular)
- Matrix operations: addition, subtraction, scalar multiplication, and matrix multiplication
- Properties of matrix operations (associativity, distributivity, non-commutativity)
- Transpose of a matrix and its properties
- Trace of a square matrix
Chapter 2: Determinants and Matrix Inverse
This chapter focuses on determinants and the inverse of a matrix, including:
- Definitions
- Properties of determinants
- Calculation of determinants using Gauss elimination (row reduction to triangular form) - Inverse of a matrix using the adjoint (cofactor) method
- Inverse of a matrix using the Gauss-Jordan elimination method
Chapter 3: Systems of Linear Equations
This chapter covers methods for solving linear systems, including:
- Matrix representation of linear systems
- Classification of systems: Cramer systems and non-Cramer systems
- Solving Cramer systems using
- Solving non-Cramer systems
Chapter 4: Eigenvalues, Eigenvectors, and Diagonalization
This chapter introduces advanced concepts of linear transformations, including:
- Definition of eigenvalues and eigenvectors
- Characteristic polynomial
- Finding eigenvalues
- Finding eigenvectors