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ECON2019 : Matrix Algebra for Business and Social Sciences

Course Objective  This course provides an introduction to some of the more important topics in the field of Matrix Algebra. Matrix Algebra has widespread applications in the fields of Economics, Psychology and Sociology. Therefore it is essential for students majoring in any of the aforementioned fields to have a working knowledge of Matrix Algebra. This course also provides students with an excellent introduction to some of the abstract concepts that underpin much of modern mathematics. Although considerable emphasis will be placed on the computational aspects of Matrix Algebra, students will learn how to provide proofs for some of the basic algebraic facts that will be encountered during the course.   Course Outline Systems of Linear Equations   1.1  Elementary row operations 1.2  Gaussian Elimination 1.3  Augmented Matrices and Echelon Form 1.4  Homogeneous systems   Matrix Algebra 2.1  Matrix Operations 2.2  Algebraic Properties of Matrices 2.3  Inverse of a Matrix   Real Vector Spaces 3.1  Vectors in 3-space 3.2  Vector Spaces 3.3  Subspaces 3.4  Linear Independence 3.5  Basis and Dimension 3.6  Rank and Nullity 3.7  Introduction to Linear Transformations   Determinants 4.1  Properties of Determinants 4.2  Cofactor Expansion 4.3  Inverse of a matrix 4.4  Cramer’s Rule   Eigevalues and Eigenvectors 5.1  The Eigenvalue Problem 5.2  Eigenvalue and Eigenvectors 5.3  Cayley-Hamilton Theorem 5.4  Applications of Eigenvalues and Eigenvectors   Quadratic Forms 6.1  Real Quadratic Forms 6.2  Positive Definiteness 6.3  Rank, Index and Signature 6.4  Applications of Quadratic Forms Prescribed Texts   Hoy, M, Mathematics for Economics, MIT Press, Massachusetts . Hoy, M, Mathematics for Economics: Student Solutions Manual, MIT Press, Massachusetts . Recommended Texts Kolman, B and Hill, D, Elementary Linear Algebra, 7th edition, Prentice Hall, New Jersey