Course Title: Linear Algebra
Type of Course: Compulsory, Theory, Non-departmental
Offered to: EEE
Pre-requisite Course(s): None
Definition of matrices. Algebra of matrices. Transpose of a matrix and inverse of a matrix. Factorization. Determinants. Quadratic forms. Matrix polynomials. Eigenvalues and eigenvectors. Diagonalization.
Introduction to systems of linear equations. Gaussian elimination. Euclidean n-space. Linear transformations from IRn to IRm. Properties of' linear transformations from IRn to IRm. Real vector spaces and subspaces. Basis and Dimension. Row space, column space and null space. Rank and Nullity. Inner products. Angle and orthogonality in inner product spaces. Orthogonal basis: Gram-Schmidt process and QR-Decomposition. Linear transformations: Kernel and Range. Application to Computed Tomography and electric networks.
To understand the fundamental properties of matrices including determinants, inverse matrices, matrix factorizations, eigenvalues, eigenvectors along with their application, and linear transformations; understanding the basic concepts of the system of linear equations and apply the matrix calculus to solve linear systems of equations.
To comprehend the Euclidean n-space, vector spaces, subspaces, linear span, and determine the basis and dimension of vector spaces.
Familiarity with basic properties of matrix and determinants, fundamental concepts of set theory, real and complex number system, and preliminary knowledge of geometry and precalculus.
| CO No. | CO Statement | Corresponding PO(s)* | Domains and Taxonomy level(s) | Delivery Method(s) and Activity(-ies) | Assessment Tool(s) |
|---|---|---|---|---|---|
| 1 | Understand the fundamental concepts and methods of Matrix Algebra to solve linear and non- linear system of equations. | PO(b) | C2 | Lectures, Homework | Written exams; assignment |
| 2 | Apply the idea of rank, eigen values and eigen vector space and quadratic problem in real- life situations. | PO(a) | C3 | Lectures, Homework | Written exams; assignment |
| 3 | Explain vector space, subspace, inner products, their uses and apply to some relevant problems | PO(a) | C2 | Lectures, Homework | Written exams; assignment |
* Cognitive Domain Taxonomy Levels: C1 – Knowledge, C2 – Comprehension, C3 – Application, C4 – Analysis, C5 – Synthesis, C6 – Evaluation, Affective Domain Taxonomy Levels: A1: Receive; A2: Respond; A3: Value (demonstrate); A4: Organize; A5: Characterize; Psychomotor Domain Taxonomy Levels: P1: Perception; P2: Set; P3: Guided Response; P4: Mechanism; P5: Complex Overt Response; P6: Adaptation; P7: Organization
Program Outcomes (PO): PO(a) Engineering Knowledge, PO(b) Problem Analysis, PO(c) Design/development Solution, PO(d) Investigation,
PO(e) Modern tool usage, PO(f) The Engineer and Society, PO(g) Environment and sustainability, PO(h) Ethics, PO(i) Individual work and team work,
PO(j). Communication, PO(k) Project management and finance, PO(l) Life-long Learning
* For details of program outcome (PO) statements, please see the departmental website or course curriculum
| K1 | K2 | K3 | K4 | K5 | K6 | K7 | K8 | P1 | P2 | P3 | P4 | P5 | P6 | P7 | A1 | A2 | A3 | A4 | A5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Weekly Schedule for Linear Algebra
| Weekly plan for course content and mapping with COs | |
|---|---|
| Weeks | Topics |
| Week-1 to 2 | Types of matrices and algebraic properties, Inverse of a matrix, rank of a matrix, elementary transformations, Factorization Row-reduce a matrix to either row-echelon or reduced row-echelon form. |
| Week-3 to 4 | Introduction to system of linear equations, Gaussian elimination, Quadratic forms, Matrix polynomials. Eigen values and Eigenvectors. |
| Week- 5 to 8 | Euclidean n-space. Linear transformations from IRn to IRm. Properties of' linear transformations from IRn to IRm. Real vector spaces and subspaces. Basis and Dimension. Rank and Nullity. |
| Week-9 to 10 | Inner product spaces. Angle and orthogonality in inner product spaces. Linear transformations: Kernel and Range. |
| Week-11 to 12 | Orthogonal basis: Gram-Schmidt process and QR-Decomposition. |
| Week-13 | Application of linear algebra related to Engineering disciplines. |
| Week-14 | Class Test |
Class Participation: Class participation and attendance will be recorded in every class.
Continuous Assessment: Continuous assessment in any of the activities such as quizzes, assignment, presentation, etc. The scheme of the continuous assessment for the course will be declared on the first day of classes.
Final Examination: A comprehensive term final examination will be held at the end of the Term following the guideline of academic Council.
Class Participation 10%
Continuous Assessment 20%
Final Examination 70%
Total 100%
Advanced Engineering Mathematics by Erwin Kreyszig, Herbert Kreyszig and Edward J. Norminton.
Elementary Linear Algebra: Applications Version by Howard Anton and Chris Rorres.
Introduction to linear Algebra by Gilbert Strang.
Theory and Problems of Linear Algebra (Schaum’s Outline Series) by Seymour Lipschutz.
Advanced Engineering Mathematics, S. Chand Publishing, H. K. Dass.
Elementary Linear Algebra with Applications by Bernard Kolman.