Rank of a Matrix | Part 1 | Minor Method & Introduction | B.Sc & B.Tech Maths Sem I | MWSB

📘 MATHS WITH SANDEEP BHATT (MWSB) Powered by Om Science Classes, Ranchi (Jharkhand) 🎓 Course: B.Sc. Mathematics (Honours) – Semester I 🏛️ University: Ranchi University (As per NEP–FYUGP Curriculum 2025–26 onwards) 📖 Chapter: Rank of a Matrix 📍 Topic (Part 1): Introduction & Minor Method 👨‍🏫 Educator: Sandeep Bhatt Sir (Mathematics Educator | Founder – Om Science Classes) ────────────────────────────────────────── 📖 ABOUT THIS LECTURE (PART 1) In this lecture, we begin the topic Rank of a Matrix, one of the most fundamental concepts in Linear Algebra. You will understand: • What minors are • How to find minors of 1×1, 2×2, and 3×3 • How rank is defined using non-zero minors • Why rank is essential for solving linear systems • The complete Minor Method for 3×3 matrices This is the most important conceptual class, forming the base for later videos on echelon forms and row operations. ────────────────────────────────────────── 🧠 TOPICS COVERED IN PART 1 1️⃣ Meaning of Minors (Order 1, 2, 3) 2️⃣ Definition of Rank using Minors 3️⃣ Rank = Largest order of a non-zero minor 4️⃣ Important observations about rank 5️⃣ Strategy to find rank of 3×3 matrices 6️⃣ Examples based on the Minor Method • Example 1 – Rank = 3 • Example 2 – Rank = 2 • Example 3 – Rank of a 3×4 matrix ────────────────────────────────────────── 📌 KEY POINTS YOU WILL LEARN • How to compute rank quickly using minors • How to identify non-zero determinants • How minors control the dimension of row/column space • When a matrix is singular vs non-singular • Why minor method is best for small matrices ────────────────────────────────────────── 🧩 SOLVED EXAMPLES IN THIS LECTURE ✔ Example (i): Rank of [1 2 2; 2 3 4; 0 2 2] → rank = 3 ✔ Example (ii): Rank of [2 3 4; 3 1 2; –1 2 2] → rank = 2 ✔ Example (iii): Rank of [1 1 –1 1; 1 –1 2 –1; 3 1 0 1] → rank = 2 ────────────────────────────────────────── 🎯 LEARNING OUTCOMES After this lecture, students will be able to: ✔ Compute rank using non-zero minors ✔ Understand minor structures clearly ✔ Decide singular/non-singular nature of a matrix ✔ Approach higher-order matrices confidently ────────────────────────────────────────── 🏛 COURSE DETAILS • Semester: I • Subject: Linear Algebra (Matrix Theory) • Mode: Online + Offline (Hybrid Learning) • Platform: Maths With Sandeep Bhatt (MWSB) • Location: Ranchi, Jharkhand ────────────────────────────────────────── 👨‍🏫 INSTRUCTOR DETAILS Sandeep Bhatt Sir Mathematics Educator | Founder – Om Science Classes 📍 Ranchi, Jharkhand 📞 Contact: 7903262149 ────────────────────────────────────────── 🔗 FOLLOW & CONNECT 📺 YouTube: Maths With Sandeep Bhatt (MWSB) 📘 Instagram: @omscienceclasses 📗 Facebook: Om Science Classes Ranchi ────────────────────────────────────────── 🙏 THANK YOU FOR WATCHING! If you found this lecture helpful, please LIKE, SHARE & SUBSCRIBE to the channel Maths With Sandeep Bhatt (MWSB) for high-quality Mathematics lectures. ────────────────────────────────────────── 📊 SEO KEYWORDS rank of a matrix, minor method rank, matrix rank explained, bsc maths semester 1, ranchi university maths, linear algebra rank, minor of a matrix, rank definition, matrix theory nep fyugp, sandeep bhatt sir maths, om science classes, maths with sandeep bhatt ────────────────────────────────────────── #MathsWithSandeepBhatt #MWSB #OmScienceClasses #RankOfMatrix #MinorMethod #LinearAlgebra #BScMathematics #RanchiUniversity #NEP2025 #Semester1 #MatrixTheory