Rank of a Matrix | Normal Form (Part 5) | Full Solved Examples | B.Sc/B.Tech Maths | MWSB

📘 MATHS WITH SANDEEP BHATT (MWSB)
Powered by Om Science Classes – Ranchi, Jharkhand
🎓 COURSE:
B.Sc. Mathematics (Honours) | B.Tech Engineering Mathematics
Chapter: Rank of a Matrix
Topic (Part 5): Reduction to Normal Form (Canonical Form) – Full Solved Examples
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📖 ABOUT THIS LECTURE
In Part 5, we learn how to reduce any matrix to its Normal Form / Canonical Form
using both row and column elementary transformations.
You will clearly understand:
✔ What is Normal Form (Canonical Form)
✔ How Iᵣ (Identity Submatrix) determines rank
✔ Pivot positions and identity block formation
✔ Why row + column operations do NOT change rank
✔ Complete step-by-step solved examples (Part 5)
This method is universally used in Linear Algebra and appears in:
• B.Sc. Maths Honours (Semester I / III)
• B.Tech Engineering Mathematics
• JUT Engineering Mathematics
• NEP–FYUGP 2024–25 Syllabus
• Competitive Exams (IIT JAM, CUET, CSIR NET basics)
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🧠 TOPICS COVERED IN PART 5
1️⃣ Elementary Row & Column Operations
2️⃣ Pivot Selection and Identity Block Formation
3️⃣ Reduction to Canonical Form:
A → [ Iᵣ 0 ]
[ 0 0 ]
4️⃣ Rank Determination: ρ(A) = r
5️⃣ Full Solved Examples:
• Example 1
• Example 2
• Example 3
• Example 4
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🏛️ UNIVERSITY ALIGNMENT
• Ranchi University
• Jharkhand University of Technology (JUT)
• NEP–FYUGP Mathematics Curriculum
Perfect for Engineering & B.Sc students!
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👨‍🏫 ABOUT THE INSTRUCTOR
Sandeep Bhatt Sir
(Mathematics Educator | Founder – Om Science Classes)
Specialist in: Linear Algebra, Calculus, Differential Equations
📞 Contact: 7903262149
📍 Ranchi, Jharkhand
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