To succeed in this course you will need to be comfortable with vectors, matrices, and three-dimensional coordinate systems.

Learning Outcomes

At the end of this course the student will be able to:

• Solve linear systems of equations
• Comprehend vector spaces, subspaces and inner product spaces
• Understand fundamental properties of matrices including determinants, inverse matrices, matrix factorizations, eigenvalues, orthogonality and diagonalization
• Have an insight into the applicability of linear algebra
• Criticallyanalyze and construct mathematical arguments that relate to the study of introductory linear algebra.

Contents

1. Introduction to Vectors: Vectors and Linear Combinations, Lengths and Dot Products, Matrices.
2. Solving Linear Equations: Vectors and Linear Equations, the Idea of Elimination, Elimination Using Matrices, Rules for Matrix Operations, Inverse Matrices.
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.
5. Orthogonally: Orthogonally of the Four Subspaces, Projections, Least Squares Approximations, Orthogonal Bases and Gram-Schmidt.
6. Determinants: The Properties of Determinants, Permutations and Cofactors, Cramer's Rule, Inverses, and Volumes.
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). 
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.
10. Complex Vectors and Matrices: Complex Numbers, Hermitian and Unitary Matrices, Matrix Factorizations.
Textbook(s)

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

Reference Material

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

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

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

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

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

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

Suggested Books

1. Linear Algebra by David Cherney, Tom Denton, Rohit Thomas and Andrew Waldron.
2.  Linear Algebra and Its Applications by David C Lay and Steven R Lay. 
3. Schaum’s Outline of Theory and Problem of Linear Algebra. Seymour Lipschutz. Mc-Graw Hill. 

ASSESSMENT CRITERIA

Sessional: 20 (Presentation / Assignment 10, Attendance 05, Quiz 05) 

Mid-Term Exam:  30

Final-Term Exam: 50

Class :BSIT 3rd Regular 

Program: BSIT

Session:2019-2023

Key Dates and Time of Class Meeting

Wednesday-Thursday                                                               8:00AM-9:30AM

Commencement of Classes                                                   October 12, 2020

Mid Term Examination                                                            December 14-18 2020 

Final Term Examination                                                          February 08-12, 2021

Declaration of Result                                                              February 19, 2021