Скачать или смотреть Eigenvalues and Eigenvectors | Lecture 20 | Linear Algebra Explained Step by Step

Eigenvalues and Eigenvectors | Lecture 20 | Linear Algebra Explained Step by Step
#eigenvalue #eigenvector #linearalgebra

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In this video, we will dive into one of the most important and powerful concepts of Linear Algebra — Eigenvalues and Eigenvectors. These ideas play a crucial role in advanced mathematics, physics, computer science, and engineering.

Whether you are a college/university student, preparing for F.Sc / ICS, or learning linear algebra for entry tests or academic clarity, this lecture is designed to give you a strong foundation in this topic with step-by-step explanation in Urdu + English mix.

🎯 What You’ll Learn in This Video:
✅ What are Eigenvalues and Eigenvectors
✅ How to find Eigenvalues from the characteristic equation
✅ How to calculate the determinant of 𝐴−𝜆𝐼
✅ How to find Eigenvectors using the equation (𝐴−𝜆𝐼)𝑋=0
✅ Solved examples for 2×2 and 3×3 matrices
✅ Real-life applications of eigenvalues in various fields
✅ Board exam tips and tricks for better understanding

📌 Language: Urdu + English Mix
📚 Level: 11th / 12th Class | ICS | BSc | University | ECAT | NUST | NUMS | Entry Test

🧠 Why This Topic is Important:
-Eigenvalues and eigenvectors are used in:
-Solving systems of differential equations
-Computer graphics & machine learning
-Quantum mechanics
-Principal component analysis (PCA)
-Vibration analysis in engineering

🧮 Related Topics You Should Watch:
-Determinants and Inverse of a Matrix
-Diagonalization of Matrices
-Rank and Nullity
-Linear Transformation Basics

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