6111 Linear Algebra

Course Description

1.Matrices: Definition and Notation, Matrix Algebra, Terminology and Notation for Systems of Linear Equations, Elementary Row Operations and Row-Echelon Matrices, Gaussian Elimination, Gauss-Jordan Elimination, Elementary Matrices and the LU Factorization.
2.Determinants: The Definition of a Determinant, Properties of Determinants, Cofactor Expansions, Cramer’s Rule.
3.Vectors: fundamental Concepts of Vectors, Vector Product of two Vectors, Angle between of two vectors, Cross Product of two Vectors, Work Done by Force using Dot Product of two Vectors.

Learning Objective

• At the end of the semester, students should know basic concepts of matrices and they enable to solve systems by using different methods such as Gaussian Elimination, Gauss-Jordan Elimination, and Inverse of a Square Matrix. We expect that the students should able to use some properties of determinant and students will use it to solve linear systems. They are also expected to work out some operations of vectors such as dot product of vectors and cross product of two Vectors.

3

Books for this Course

• 1.Differential Equations and Linear Algebra STEPHEN W. GOODE
• 2.Vector Analysis (Copy)

Times Offered

• September 2014
• January 2015

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