# Linear Algebra - Syllabus

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

Linear equations in linear Algebra

1.1    Systems of linear equations

1.2    Row reduction and Echelon Forms

1.3    Vector equations

1.4    The matrix equations Ax = b

1.5    Solution sets of linear systems

1.6    Linear independence

1.7    Introduction Linear Transformations

1.8    The matrix of a Linear Transformations

Matrix Algebra

2.1    Matrix operations

2.2    The inverse of a matrix

2.3    Characterization of invertible matrices

2.4    Partitioned Matrices

2.5    The Leontief Input-output model

2.6    Application to Computer graphics

Determinants

3.1    Introduction to determinants

3.2    Properties of determinants

3.3    Cramer's rule value and linear transformations

Vector Spaces

4.1    Vector spaces and sub polar

4.2    Null spaces, Column spaces and linear transformations

4.3    Linearly Independent Sets; Bases

4.4    Coordinate systems

4.5    The dimension of a vector space

4.6    Rank

4.7    Change of basis

Eigen values and Eigen vectors

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

Orthogonality and Least Squares

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