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Tribhuvan university CSIT 2065 Syllabus Linear Algebra

Linear Algebra - Syllabus

Course Overview and Structure
Syllabus Notes Old Questions Unit Wise Questions Question Bank

Embark on a profound academic exploration as you delve into the Linear Algebra course () within the distinguished Tribhuvan university's CSIT department. Aligned with the 2065 Syllabus, this course (MTH-155) seamlessly merges theoretical frameworks with practical sessions, ensuring a comprehensive understanding of the subject. Rigorous assessment based on a 80+20 marks system, coupled with a challenging passing threshold of , propels students to strive for excellence, fostering a deeper grasp of the course content.

This 3 credit-hour journey unfolds as a holistic learning experience, bridging theory and application. Beyond theoretical comprehension, students actively engage in practical sessions, acquiring valuable skills for real-world scenarios. Immerse yourself in this well-structured course, where each element, from the course description to interactive sessions, is meticulously crafted to shape a well-rounded and insightful academic experience.


Course Synopsis: Linear equations in linear algebra, Matrix algebra, Determinants,  Vector spaces, Eigen values and Eigen vectors. Orthogonality and least squares. Symmetric matrices and Quadratic forms.
Goal: This course provides students with the knowledge of fundamental of linear algebra and the theory of matrices. On completion of this course the student will master the basic concepts and acquires skills in solving problems in linear algebra.

Units

Key Topics

  • Systems of Linear Equations
    LI-1.1

    This topic covers the basics of systems of linear equations, including definitions, examples, and methods for solving them.

  • Row Reduction and Echelon Forms
    LI-1.2

    This topic explores the techniques of row reduction and echelon forms, including Gaussian elimination and its applications.

  • Vector Equations
    LI-1.3

    This topic introduces vector equations, including their definitions, properties, and applications in linear algebra.

  • Matrix Equations
    LI-1.4

    This topic covers matrix equations of the form Ax = b, including their solutions, properties, and applications.

  • Solution Sets of Linear Systems
    LI-1.5

    This topic examines the solution sets of linear systems, including the null space, column space, and row space.

  • Linear Independence
    LI-1.6

    This topic explores the concept of linear independence, including definitions, examples, and applications in linear algebra.

  • Introduction to Linear Transformations
    LI-1.7

    This topic introduces linear transformations, including their definitions, properties, and applications in linear algebra.

  • The Matrix of a Linear Transformation
    LI-1.8

    This topic covers the matrix representation of linear transformations, including its properties and applications.

Key Topics

  • Machine Translation
    MA-01

    Exploring the concept of machine translation, including AI and expert systems, with a focus on cause and effect language skills.

  • Multi Media
    MA-02

    Understanding computer-to-video conversion and its applications, with a focus on making predictions language skills.

  • Computer Graphics
    MA-03

    Learning about 24-bit color and its role in computer graphics, with a focus on letter writing language skills.

  • Basic Mail Server Configuration
    MA-04

    Configuring popular mail servers such as Sendmail, Postfix, Qmail, and Exim, including setup and basic configuration.

  • SPAM Control and Filtering
    MA-05

    Implementing effective SPAM control and filtering techniques to prevent unwanted emails and improve mail server security.

  • Troubleshooting Mail Servers
    MA-06

    Identifying and resolving common issues and errors in mail server configuration and operation.

3.1    Introduction to determinants                       

3.2    Properties of determinants                 

3.3    Cramer's rule value and linear transformations     

Key Topics

  • Vector Spaces and Subspaces
    VE-1

    Introduction to vector spaces and subspaces, including their definitions and properties.

  • Null Spaces, Column Spaces, and Linear Transformations
    VE-2

    Exploration of null spaces, column spaces, and linear transformations, including their relationships and applications.

  • Linearly Independent Sets and Bases
    VE-3

    Discussion of linearly independent sets and bases, including their definitions, properties, and importance in vector spaces.

  • Coordinate Systems
    VE-4

    Introduction to coordinate systems, including their definition, importance, and applications in vector spaces.

  • Dimension of a Vector Space
    VE-5

    Exploration of the dimension of a vector space, including its definition, properties, and importance.

  • Rank
    VE-6

    Discussion of rank, including its definition, properties, and importance in linear algebra.

  • Change of Basis
    VE-7

    Introduction to change of basis, including its definition, importance, and applications in linear algebra.

5.1    Eigen vectors and Eigen values                    

5.2    The characteristics equations                       

5.3    Diagonalization               

5.4    Eigen vectors and Linear Transformations             

5.5    Complex Eigen values             

5.6    Discrete Dynamical System 

6.1    Linear product, length and Orthogonality            

6.2    Orthogonal sets             

6.3    Orthogonal Projections            

6.4    The Gram- Schmidt process               

6.5    Least square problems             

6.6    Applications to Linear models