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(01)Find the eigen values and associated eigen vectors of the following matrices. 0 1 b. GD) a. 1 2 (²²)

(01)Find the eigen values and associated eigen vectors of the following matrices. 0 1 b. GD) a. 1 2 (²²)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(01)Find the eigen values and associated eigen vectors of the following matrices. 1 2. (27) a. b. (1) (02)Use the Jacobi iteration method and find first five approximations to the solutions of the following systems. Use X) = (0, 0, 0)¹. a. 10x₁ + x₂x3 = 12 2x₁ + 15x₂ + 3x3 = 14 3x₁ + 5x₂ + 25x3 = -17 b. 10x₁ + 3x₂ + x3 = 14 2x₁10x₂ + 3x3 = -5 x₁ + 3x₂ + 10x3 = 14 (03)Use the Gauss-Seidel iteration method and find first five approximations to the solutions of the following systems. Use X(0) = (0, 0, 0)t. a. 10x₁ + x₂x3 = 12 2x₁ + 15x₂ + 3x3 = 14 3x₁ + 5x₂ + 25x3 = -17 b. 10x₁ + 3x₂ + x3 = 14 2x₁10x₂ + 3x3 = -5 X₁ + 3x₂ +10x3 = 14
Transcribed Image Text:(01)Find the eigen values and associated eigen vectors of the following matrices. 1 2. (27) a. b. (1) (02)Use the Jacobi iteration method and find first five approximations to the solutions of the following systems. Use X) = (0, 0, 0)¹. a. 10x₁ + x₂x3 = 12 2x₁ + 15x₂ + 3x3 = 14 3x₁ + 5x₂ + 25x3 = -17 b. 10x₁ + 3x₂ + x3 = 14 2x₁10x₂ + 3x3 = -5 x₁ + 3x₂ + 10x3 = 14 (03)Use the Gauss-Seidel iteration method and find first five approximations to the solutions of the following systems. Use X(0) = (0, 0, 0)t. a. 10x₁ + x₂x3 = 12 2x₁ + 15x₂ + 3x3 = 14 3x₁ + 5x₂ + 25x3 = -17 b. 10x₁ + 3x₂ + x3 = 14 2x₁10x₂ + 3x3 = -5 X₁ + 3x₂ +10x3 = 14
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