Subspace One Shot🔥 | NET GATE JAM 🚀| Direct Sum + 50+ Problems | Linear Algebra | Zero to Advanced

Subspace One Shot🔥 | NET GATE JAM 🚀| Direct Sum + 50+ Problems | Linear Algebra | Zero to Advanced 🔥Lecture Slides:-🚀 https://www.linkedin.com/posts/md-sah... One Video. Complete Subspace. Zero Confusion. 🚀 If you are preparing for CSIR NET, GATE, IIT JAM, TIFR or MSc Mathematics exams, this lecture will make your Subspace concepts crystal clear from basics to advanced level. 00:00 Introduction 00:24 Contents 00:50 Introduction to Subspace 01:04 Applications of Subspaces 02:41 Understanding the Concept of Subspace 06:01 Definition of Subspace 07:04 Important Observation: Trivial, Proper & Improper Subspaces 17:00 Important Theorems on Subspaces (Overview) 17:46 Motivation Behind the Necessary & Sufficient Condition Theorem 20:14 Theorem 1: Necessary and Sufficient Condition for a Subspace 42:51 Problems on Subspaces 43:03 Problem 1 50:39 Problem 2 51:18 Problem 3 53:43 Problem 4 1:04:26 Problem 5 1:09:31 Problem 6 1:16:20 Problem 7 1:16:59 Problem 8 1:17:13 Shortcut Trick for Checking Subspaces 1:20:25 Problem 8 (Continued) 1:33:03 Special Notes 1 1:34:34 Problem 9 1:35:00 Short Trick for Subspace Problems 1:35:53 Problem 9 (Continued) 1:44:33 Special Questions List 1:54:11 Problem 10 2:00:30 Problem 11 2:22:44 Problem 12 2:25:21 Problem 13 2:26:27 Problem 14 2:31:44 Problem 15 2:40:37 Problem 16 2:47:17 Problem 17 2:57:38 Problem 18 3:00:30 Problem 19 3:00:47 Problem 20 3:01:51 Problem 21 3:04:03 Problem 22 3:10:16 Problem 23 3:11:37 Problem 24 3:15:24 Special Notes 2 3:16:06 Theorems on Subspaces (Continued) 3:16:50 Theorem 2 3:28:53 Theorem 3 3:39:24 Theorem 4 3:59:55 Theorem 5 (Direct Sum Related Theorem, we will prove it after some time in the same lecture) 4:00:34 Theorem 6 4:12:45 Theorem 7 4:17:20 Problem 25 4:24:16 Problem 26 4:24:48 Problem 27 4:25:59 Problem 28 4:41:17 Problem 29 4:58:56 Problem 30 5:07:17 Problem 31 5:16:49 Problem 32 5:17:18 Problem 33 5:17:57 Problem 34 5:19:20 Problem 35 5:19:27 Problem 36 5:20:28 Problem 37 5:21:40 Problem 38 5:21:56 Problem 39 5:22:08 Problem 40 5:23:49 Problem 41 5:23:58 Problem 42 5:24:02 Problem 43 5:24:13 Problem 44 5:25:12 Problem 45 5:28:34 Problem 46 5:39:05 Problem 47 5:42:16 Problem 48 5:44:03 Direct Sum of Subspaces (Start) 5:44:13 Why Do We Need Direct Sum? (Intuition & Motivation) 5:55:26 Definition of Direct Sum of Subspaces 5:59:01 Problem 49 (Question 1 on Direct Sum) 6:05:07 Problem 50 (Question 2 on Direct Sum) 6:06:59 Problem 51 (Question 3 on Direct Sum) 6:11:49 Problem 52 (Question 4 on Direct Sum) 6:15:48 Problem 53 (Question 5 on Direct Sum) 6:26:01 Theorem 8 (Theorem 1 on Direct Sum) 6:44:22 Modular Law 6:46:03 Problems on Modular Law 6:46:23 Quiz (Test your knowledge) 6:48:21 Summary of this lecture 6:52:36 References (SK Mapa, Friedberg, Dr. AP Singh) 6:54:40 Thank You & Outro In this 7 Hours Masterclass, we cover complete theory, proofs, tricks, examples and 50+ exam-oriented problems. 📌 What You Will Learn: ✅ Concept of Subspace from Basics ✅ How to Check Any Subspace Easily ✅ Subspace Test & Important Results ✅ Standard Examples & Counterexamples ✅ Sum of Subspaces ✅ Direct Sum of Subspaces ✅ Previous Exam Level Problems 📚 Standard References & Problems Covered From: ✔ Friedberg – Linear Algebra ✔ S.K. Mapa – Linear Algebra ✔ A.P. Singh – Linear Algebra 🎯 Highly Recommended For: • CSIR NET Mathematics • GATE Mathematics • IIT JAM Mathematics • TIFR | ISI | CMI • B.Sc & M.Sc Mathematics Students Why watch this lecture? ✔ Complete Concept Clarity ✔ Beginner Friendly Explanation ✔ Advanced Level Questions ✔ Standard Book Approach 👨‍🏫 Educator: Muhammad Sahwaj Raza M.Sc Applied Mathematics National Institute of Technology Warangal (NITW) Welcome to MathDil ❤️ Where Mathematics Meets Understanding. 📚 Subjects Covered on MathDil: Linear Algebra | Real Analysis | Abstract Algebra | Complex Analysis | Topology | Functional Analysis | ODE | PDE | Numerical Analysis Subscribe & Start Your Mathematical Journey 🚀