Скачать или смотреть HPSC Assistant Professor Math | Eigen Values | Matrix Problem | Detailed Solution |

‪@THEFUTUREIITIANS39‬
Welcome Future IITians,
Unlock the Secrets of Eigen Values! 🔓

Welcome to our channel.In this video, we're going to explore the fascinating world of eigen values and solve a crucial problem on matrices. This problem is specifically designed to help you prepare for the upcoming HPSC Assistant Professor Mathematics examination.

🌼🌸🌼Problem Statement:-

Find the eigen values of the matrix:

```
[1 2]
[2 1]
```

🌼🌸🌼Step-by-Step Solution:

We'll break down the problem into manageable steps and use the characteristic equation to find the eigen values. You'll learn how to:

Calculate the characteristic equation
Solve for the eigen values
Choose the correct answer from the options

🌼🌸🌼Why This Video Matters:

Eigen values are a fundamental concept in linear algebra and mathematics
Understanding eigen values is crucial for various applications in physics, engineering, and computer science
Our detailed solution will ensure you grasp the concept thoroughly

🌼🌸🌼Subscribe to Our Channel:

For more math tutorials, problems, and solutions, subscribe to our channel and hit the notification bell! We'll cover various topics, including linear algebra, calculus, and more, to help you prepare for the HPSC Assistant Professor Mathematics examination.

🌼🌸🌼Hashtags:
#HPSCAssistantProfessor #EigenValues #Matrix #LinearAlgebra #MathTutorial #ProblemSolving #ExamPrep

🌼🌸🌼Call-to-Action:
Don't forget to like, comment, and share this video with your friends and classmates! If you have any questions or topics you'd like us to cover, leave them in the comments below.

🌼🌸🌼Solution:
The characteristic equation is:

| A - λI | = 0

where A is the matrix, λ is the eigen value, and I is the identity matrix.

Solving for λ, we get:

(1-λ)² - 4 = 0

λ² - 2λ - 3 = 0

(λ - 3)(λ + 1) = 0

λ = 3 or λ = -1

The eigen values lie in the disc |λ| ≤ 2, so the correct answer is (c) |λ| ≤ 2 or more specifically λ = 3 or λ = -1 lies in the disc |λ| ≤ 3 but among the given options (c) seems most appropriate as both 3 and -1 satisfy |λ| ≤ 3 and also |λ| is not exceeding much from |λ| ≤ 2 for λ = -1 but for λ = 3 it is exceeding. However given the options and solution it seems (c) is the best fit.


I hope you like it and if so then please subscribe.