Rank, Properties & Rank-Nullity Theorem | Linear Algebra Lec 07

RANK, PROPERTIES & RANK-NULLITY THEOREM | LINEAR ALGEBRA LEC 07 🚀 MASTER LINEAR ALGEBRA FOR GATE & BEYOND! In this lecture, we explore one of the most important concepts in Linear Algebra: the Rank of a matrix. We discuss how to calculate Rank using Echelon forms, dive into its essential properties, and master the Rank-Nullity Theorem—a frequent favorite in GATE DA (Data Science & AI) and GATE CSE (Computer Science) exams. 📘 FREE GATE DA/CSE TEXTBOOK Download at 👉 https://gatexaiml.in 📝 TOPICS COVERED IN THIS SESSION: ● Rank of a Matrix: Definition and calculation using Row Echelon Form (REF). ● Rank Properties: Understanding Rank(A), Rank(A transpose), and Rank of product matrices. ● Elementary Transformations: Why row operations do not change the rank. ● Rank-Nullity Theorem: The fundamental relation: Rank(A) + Nullity(A) = Number of Columns. ● Dimension of Subspaces: Connecting Rank to the dimension of Column and Row spaces. 🎓 WHO SHOULD WATCH? ✔ GATE Aspirants: This is a high-yield topic for both GATE DA and CSE technical papers. ✔ University Students: Essential for B.Tech/B.Sc Mathematics and Linear Algebra courses. ✔ Data Science Learners: Crucial for understanding Linear Independence and Feature Selection. ✔ Competitive Exams: Important for ESE, ISRO, and BARC technical rounds. 📚 WATCH FULL PLAYLISTS: 🔹 GATE DA | Matrices & Linear Algebra Playlist:    • GATE DA Matrices and Linear Algebra   🔹 GATE CSE | Matrices & Linear Algebra Playlist:    • GATE CSE - Matrices and Linear Algebra   💡 Explore more resources, Mock Tests, and free textbooks at: https://gatexaiml.in #GATE #GATEDA #GATECSE #LinearAlgebra #RankOfMatrix #RankNullityTheorem #Nullity #MatrixProperties #EngineeringMathematics #DataScience #MachineLearning #AILearning #GATE2026 #MathForML #BTechMaths