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)
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📖 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.
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🧠 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
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📌 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
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🧩 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
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🎯 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
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🏛 COURSE DETAILS
• Semester: I
• Subject: Linear Algebra (Matrix Theory)
• Mode: Online + Offline (Hybrid Learning)
• Platform: Maths With Sandeep Bhatt (MWSB)
• Location: Ranchi, Jharkhand
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👨‍🏫 INSTRUCTOR DETAILS
Sandeep Bhatt Sir
Mathematics Educator | Founder – Om Science Classes
📍 Ranchi, Jharkhand
📞 Contact: 7903262149
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🔗 FOLLOW & CONNECT
📺 YouTube: Maths With Sandeep Bhatt (MWSB)
📘 Instagram: @omscienceclasses
📗 Facebook: Om Science Classes Ranchi
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🙏 THANK YOU FOR WATCHING!
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Видео Rank of a Matrix | Part 1 | Minor Method & Introduction | B.Sc & B.Tech Maths Sem I | MWSB канала Maths with Sandeep Bhatt