Course Code: MATH-204

Title of the Course: Linear Algebra

Credit Hours: 3+0

Prerequisites: Calculus I

Objectives of the course:

Linear algebra is the study of vector spaces and linear transformations. The main objective of this course is to help students learn in rigorous manner, the tools and methods essential for studying the solution spaces of problems in mathematics, engineering, the natural sciences, and social sciences and develop mathematical skills needed to apply these to the problems arising within their field of study; and to various real world problems.

Course Contents:

System of Linear Equations: Representation in matrix form,matrices, operations on matrices, echelon and reduced echelon form,inverse of a matrix (by elementary row operations), solution of linear system, Gauss-Jordan method, Gaussian elimination.

Determinants: Permutations of order two and three and definitions of determinants of the same order. Computing of determinants. Definition of higher order determinants. Properties. Expansion of determinants. Vector Spaces: Definition and examples, subspaces. Linear combination and spanning set. Linearly Independent sets. Finitely generated vector spaces. Bases and dimension of a vector space. Operations on subspaces, Intersections, sums and direct sums of subspaces. Quotient Spaces. Linear mappings: Definition and examples. Kernel and image of a linear mapping. Rank and nullity. Reflections, projections, and homotheties. Change of basis. Eigen-values and eigenvectors. Theorem of Hamilton-Cayley.

Inner product Spaces: Definition and examples. Properties, Projection. Cauchy inequality. Orthogonal and orthonormal basis. Gram Schmidt Process. Diagonalization.

Recommended Books:

1. Curtis C. W., Linear Algebra, Springer 2004.

2. Apostol T., Multi Variable Calculus and Linear Algebra, 2nd ed., John Wiley and  sons, 1997.

3. Anton H., Rorres C. , Elementary Linear Algebra: Applications Version, 10th Edition, John Wiley and sons, 2010.

4. Friedberg S., Insel A., Linear Algebra, 4th Edition, Pearson Education Canada, 2003.

5. Grossman S. I., Elementary Linear Algebra, 5th Edition, Cengage Learning, 2004.

6.   Herstein I.N. Topics in Algebra, Xerox Publishing Company, 1975.

7. Dr. Malik, Mordeson J.N., Sen M.R. Fundamental of Abstract Algebra,    McGraw Hill companies, Inc. 1987.

8. Cohn P.M. Algebra, Vol.I, London: John Wiley, 1989.

9. Burton D. Abstract and Linear Algebra, Addison-Wesley publishing Co. 1986.

10. Jacobson N. Basic Algebra, Vol.II Freeman, 1989.

11. Dr. Karamat Hussain, Linear Algebra, 1st edition, 2007.