Linear algebra is the study of linear systems of equations, vector spaces, and linear transformations. Solving systems of linear equations is a basic tool of many mathematical procedures used for solving problems in science and engineering.

**Prerequisite **

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
- Critically analyze and construct mathematical arguments that relate to the study of introductory linear algebra.

**Contents**

- Introduction to Vectors: Vectors and Linear Combinations, Lengths and Dot Products, Matrices.
- Solving Linear Equations: Vectors and Linear Equations, the Idea of Elimination, Elimination Using Matrices, Rules for Matrix Operations, Inverse Matrices.
- Elimination = Factorization; A = LU, Transposes and Permutations.
- 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.
- Orthogonally: Orthogonally of the Four Subspaces, Projections, Least Squares Approximations, Orthogonal Bases and Gram-Schmidt.
- Determinants: The Properties of Determinants, Permutations and Cofactors, Cramer's Rule, Inverses, and Volumes.
- Eigenvalues and Eigenvectors: Introduction to Eigenvalues, Diagonalizing a Matrix, Applications to Differential Equations, Symmetric Matrices, Positive Definite Matrices, Similar Matrices, Singular Value Decomposition (SVD).
- 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.
- Numerical Linear Algebra: Gaussian Elimination in Practice, Norms and Condition Numbers, Iterative Methods for Linear Algebra.
- 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**

- Elementary Linear Algebra with Applications by Bernard Kolman, David Hill, 9th Edition, Prentice Hall PTR, 2007.
- Linear Algebra And Its Applications by Gilbert Strang, Strang, Brett Coonley, Andrew Bulman-Fleming, 4th Edition, 2005.
- Elementary Linear Algebra: Applications Version by Howard Anton, Chris Rorres, 9th Edition, Wiley, 2005.
- Linear Algebra and Its Applications by David C. Lay, 2nd Edition, Addison-Wesley, 2000.
- Linear Algebra by Harold M. Edwards, Birkhäuser; 1st Edition, 2004.
- Linear Algebra: A Modern Introduction by David Poole by Brooks Cole, 3rd Edition.

**Suggested Books**

- Linear Algebra by David Cherney, Tom Denton, Rohit Thomas and Andrew Waldron.
- Linear Algebra and Its Applications by David C Lay and Steven R Lay.
- 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

Monday 08:00 am - 09:30 am

wednesday 08:00 am - 09:30 am

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