W3_L3: Linear dependence

Welcome to Week 3 Lecture 3 of the course "Mathematics for Data Science II" by Prof. Sarang S Sane. Full Course: https://study.iitm.ac.in/ds/course_pages/BSMA1003.html Video Overview In this lecture, Professor Sarang Sane introduces the concept of linear dependence in vector spaces and explains how it helps in understanding the relationships among vectors. Building upon the foundational axioms of vector spaces, the lecture explores key properties such as the cancellation law of vector addition, and the uniqueness of the zero vector and additive inverses. Real-world examples, including stock-taking in a grocery shop and affine flat representations, provide geometric and intuitive insights into how vectors relate to one another. This session bridges abstract definitions with practical examples, helping learners connect mathematical theory to real data applications. About IIT Madras' online Bachelor of Science programme IIT Madras offers four-year BS programmes that aim to provide quality education to all, irrespective of age, educational background, or location. The BS programme has multiple levels, which provide flexibility to students to exit at any of these levels. Depending on the courses completed and credits earned, the learner can receive a Foundation Certificate from IITM CODE (Centre for Outreach and Digital Education), Diploma(s) from IIT Madras, or BSc/BS Degrees from IIT Madras. For more details, visit: https://www.iitm.ac.in/academics/study-at-iitm/non-campus-bs-programmes #VectorSpaces #LinearAlgebra #DataScience #Programming #Axioms #CancellationLaw #ZeroVector #AdditiveInverse #AffineFlats #StockTaking #Mathematics #OnlineLearning #BSc #VectorAddition #ScalarMultiplication #LinearDependence #Maths2 #IITMadras #MathForDataScience