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Question 5. (a) Use MATLAB to find solutions to the two systems of equations: x₁ + 3x₂ = 4 x₁ +3.00001x2 = 4.00001 represented by A₁x = b and represented by A₂y = b. Y₁ + 3y2 = 4 Y₁ +2.99999y2 = 4.00001 Analytically (not numerically) compute ||A₁ - A₂||∞ and ||x - y||. Using the concept of a condition number and relative error, explain why ||x - y||∞ is much larger than ||A₁ - A₂||-

Question 5. (a) Use MATLAB to find solutions to the two systems of equations: x₁ + 3x₂ = 4 x₁ +3.00001x2 = 4.00001 represented by A₁x = b and represented by A₂y = b. Y₁ + 3y2 = 4 Y₁ +2.99999y2 = 4.00001 Analytically (not numerically) compute ||A₁ - A₂||∞ and ||x - y||. Using the concept of a condition number and relative error, explain why ||x - y||∞ is much larger than ||A₁ - A₂||-

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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Question 5. (a) (b) (c) Use MATLAB to find solutions to the two systems of equations: x₁ + 3x₂ = 4 x₁ +3.00001x2 = 4.00001 represented by A₁x = b and represented by A₂y = b. Y₁ + 3y₂ = 4 Y₁ + 2.99999y2 = 4.00001 Analytically (not numerically) compute ||A₁ - A₂||∞ and ||x - y||.. Using the concept of a condition number and relative error, explain why ||x - y|| is much larger than ||A₁ - A2||00.
Transcribed Image Text:Question 5. (a) (b) (c) Use MATLAB to find solutions to the two systems of equations: x₁ + 3x₂ = 4 x₁ +3.00001x2 = 4.00001 represented by A₁x = b and represented by A₂y = b. Y₁ + 3y₂ = 4 Y₁ + 2.99999y2 = 4.00001 Analytically (not numerically) compute ||A₁ - A₂||∞ and ||x - y||.. Using the concept of a condition number and relative error, explain why ||x - y|| is much larger than ||A₁ - A2||00.
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