Rayleigh Power Method | Dominant Eigenvalue & Eigenvector | Question 9(c) | 1BMATE101 VTU 2025

Описание: 📘 VTU Model Question Paper–I (2025 Scheme)
1BMATE101 – Differential Calculus & Linear Algebra
First Semester B.E./B.Tech

📍 Module-4: Ordinary differential equations of higher Order

📝 Question No. 9(c)

📘 Rayleigh’s Power Method | Dominant Eigenvalue & Eigenvector | Numerical Methods | VTU

In this video, we solve a standard VTU Numerical Methods problem using Rayleigh’s Power Method to determine the dominant eigenvalue and its corresponding eigenvector for a given matrix.
This method is very important for VTU exams and frequently appears in model question papers and university examinations.

📄 Problem Statement
Determine the dominant eigenvalue and the corresponding eigenvector of the following matrix using Rayleigh’s power method:
A =
4 1 −1
2 3 −1
−2 1 5

🎯 What you will learn in this video • Concept of dominant eigenvalue
• Idea behind Rayleigh’s power method
• Step-by-step iterative procedure
• Normalization of eigenvectors
• Convergence of eigenvalues
• Final dominant eigenvalue and eigenvector
• Important VTU exam tips

✅ Why this video is useful • Explained in a simple, exam-oriented manner
• Suitable for VTU and other engineering students
• Helpful for last-minute revision
• Numerical steps clearly shown

📘📘 1BMATE101 – Engineering Mathematics
🎓 VTU 2025 Scheme | Semester 1
🔥🔥 MODEL QUESTION PAPER – I (ONE-TIME COMPLETE LIST) 🔥🔥
💯 MOST IMPORTANT | MUST WATCH | EXAM FOCUSED
📄 Covers ALL 5 MODULES
🎯 Based on latest VTU pattern
⏱️ Best for revision + exam confidence
━━━━━━━━━━━━━━━━━━━━━━━
🚨🚨 FIRST – MODEL QUESTION PAPER (COMMON FOR ALL MODULES) 🚨🚨
👉 👉    • VTU Model Question Paper–I 2025 | 1BMATE10...   👈 👈
━━━━━━━━━━━━━━━━━━━━━━━
📕 MODULE 1 – Differential Calculus ✍️📈
🔥 Most Important Playlist (Must Watch)
👉    • Module 1 Differential Calculus | Polar Cur...  
⭐ Important Playlist
👉    • Differential Calculus | VTU 1BMATE101 – Mo...  
━━━━━━━━━━━━━━━━━━━━━━━
📘 MODULE 2 – Power Series, Indeterminate Forms & Multivariable Calculus 🔁📊
🔥 Partial Differentiation | Multivariable Calculus
👉    • Partial Differentiation | Multivariable Ca...  
🔥 Maclaurin’s Series Expansion | Important VTU Problems
👉    • Maclaurin’s Series Expansion | Important V...  
🔥 Maclaurin Series – Important Problems
👉    • Maclaurin Series Important Problems  
🔥 Indeterminate Forms (1^∞) – Most Important Limits
👉    • Indeterminate Forms (1^∞) – Most Important...  
⭐ Important Playlist
👉    • Power Series, Indeterminate Forms & Multiv...  
━━━━━━━━━━━━━━━━━━━━━━━
📙 MODULE 3 – Ordinary Differential Equations 🔄📐
(First Order & First Degree, Nonlinear ODEs)
🔥 ODE | VTU 1BMATE101 – Module 3
👉    • Ordinary Differential Equations (ODE) | VT...  
🔥 Solvable for P (Differential Equations)
👉    • Solvable for P (Differential Equations)  
⭐ Important Playlist (Must Watch)
👉    • Ordinary Differential Equations (ODE) of f...  
━━━━━━━━━━━━━━━━━━━━━━━
📗 MODULE 4 – Higher Order Ordinary Differential Equations 📘➕
🔥 Most Important Playlist (Must Watch)
👉    • Higher-Order Ordinary Differential Equatio...  
━━━━━━━━━━━━━━━━━━━━━━━
📕 MODULE 5 – Linear Algebra 🧮📐
🔥 Linear Algebra Made Simple – Complete
👉    • Linear Algebra Made Simple | Rank, Consist...  
📌 Note: Gauss–Jordan Method is NOT required for this syllabus
🔥 Gauss Seidel Method & Rayleigh Power Method
👉    • Gauss Seidel method and Rayleigh power method  
⭐ Important Playlist
👉    • Linear Algebra | VTU 1BMATE101 – Module 5 ...  
━━━━━━━━━━━━━━━━━━━━━━━
📝 HOW TO USE THIS (EXAM STRATEGY) 🧠🔥
1️⃣ Watch Model Question Paper – I first
2️⃣ Identify weak modules
3️⃣ Revise module playlists
4️⃣ Rewatch Model QP before exam ⏳📖
━━━━━━━━━━━━━━━━━━━━━━━
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