Linear Algebra Course Outline - University of Sargodha

Course Title: Linear Algebra

Course Code: MATH-3215
Course Structure: Lectures: 3, Labs: 0
Credit Hours: 3
Prerequisites: None

Course Objectives:

To provide fundamentals of solution for system of linear equations, operations on system of
equations, matrix properties, solutions and study of their properties.

Course Syllabus:

Introduction to Vectors. Solving Linear Equations. Elimination = Factorization. Vector Spaces
and Subspaces. Orthogonally. Determinants. Eigenvalues and Eigenvectors. Graphs and
Networks, Markov Matrices, Population, and Economics. Linear Programming. Fourier series.
Linear Algebra for Functions, Linear Algebra for Statistics and Probability, Computer Graphics.
Numerical Linear Algebra. Complex Vectors and Matrices. Discrete Transforms and Simple
Applications.

Course Outline:

1.      Introduction to Vectors: Vectors and Linear Combinations, Lengths and Dot Products,
Matrices. [TB1: Ch. 1]

2.      Solving Linear Equations: Vectors and Linear Equations, the Idea of Elimination,
Elimination Using Matrices, Rules for Matrix Operations, Inverse Matrices. [TB1: Ch. 2]

3.      Elimination = Factorization; A = LU, Transposes and Permutations

4.      Vector Spaces and Subspaces: Spaces of Vectors, The Null space of A: Solving Ax = 0,
The Rank and the Row Reduced Form, the Complete Solution to Ax = B, Independence,
Basis and Dimension, Dimensions of the Four Subspaces. [TB1: Ch. 3]

5.      Orthogonally: Orthogonally of the Four Subspaces, Projections, Least Squares
Approximations, Orthogonal Bases and Gram-Schmidt. [TB1: Ch. 4]

6.      Determinants: The Properties of Determinants, Permutations and Cofactors, Cramer's
Rule, Inverses, and Volumes. [TB1: Ch. 5]

7.      Eigenvalues and Eigenvectors: Introduction to Eigenvalues, Diagonalizing a Matrix,
Applications to Differential Equations, Symmetric Matrices, Positive Definite Matrices,
Similar Matrices, Singular Value Decomposition (SVD). [TB1: Ch. 6]

8.      Applications: Matrices in Engineering, Graphs and Networks, Markov Matrices,
Population, and Economics; Linear Programming, Fourier series: Linear Algebra for
Functions, Linear Algebra for Statistics and Probability, Computer Graphics.

9.      Numerical Linear Algebra: Gaussian Elimination in Practice, Norms and Condition
Numbers, Iterative Methods for Linear Algebra. [TB1: Ch. 9]

10.  Complex Vectors and Matrices: Complex Numbers, Hermitian and Unitary Matrices,
Matrix Factorizations. [TB1: Ch. 10]

Textbook(s):

•          Introduction to Linear Algebra by Gilbert Strang, Wellesley Cambridge Press; 4^th Edition
(February 10, 2009). ISBN-10: 0980232716

Reference Material:

•         Elementary Linear Algebra with Applications by Bernard Kolman, David Hill, 9^th
Edition, Prentice Hall PTR, 2007. ISBN-10: 0132296543

•          Strang's Linear Algebra And Its Applications by Gilbert Strang, Strang, Brett Coonley,
Andy Bulman-Fleming, Andrew Bulman-Fleming, 4^th Edition, Brooks/Cole, 2005

•         Elementary Linear Algebra: Applications Version by Howard Anton, Chris Rorres, 9^th
Edition, Wiley, 2005.

•         Linear Algebra and Its Applications by David C. Lay, 2^nd Edition, Addison-Wesley,
2000.

•         Linear Algebra by Harold M. Edwards, Birkhauser; 1^st Edition (2004). ISBN-10:
0817643702

rd

•         Linear Algebra: A Modern Introduction by David Poole by Brooks Cole; 3 Edition
(May 25, 2010).ISBN-10: 0538735457

Note: This content is obtained from official documents of University of Sargodha and applied on BS Computer Science for Main Campus, Sub Campuses, and Affiliated Colleges.