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Practice problem 21.6 You have been given the following second order linear system and its corresponding eigenvalues: A₂ = 36 20 -16] -16 20 A₁ = 4 Guess a solution that has the form of: x = vewt And then substitute it in to (0) = z = Az Then guess what the values of v and w should be in relation to the eigenvectors and eigenvalues of matrix A. you must collect four linearly dependent solutions that are different. Note that a positive numbers square root should have both a - and + answer. Then determine the solution of the initial value problem where: [0] (0) = [8] z₁(t) €* = 2₂(t)=

Practice problem 21.6 You have been given the following second order linear system and its corresponding eigenvalues: A₂ = 36 20 -16] -16 20 A₁ = 4 Guess a solution that has the form of: x = vewt And then substitute it in to (0) = z = Az Then guess what the values of v and w should be in relation to the eigenvectors and eigenvalues of matrix A. you must collect four linearly dependent solutions that are different. Note that a positive numbers square root should have both a - and + answer. Then determine the solution of the initial value problem where: [0] (0) = [8] z₁(t) €* = 2₂(t)=

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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Practice problem 21.6 You have been given the following second order linear system and its corresponding eigenvalues: 20 -16] A₁ = 4 -16 20 Guess a solution that has the form of: * = vewt And then substitute it in to z = Az Then guess what the values of v and w should be in relation to the eigenvectors and eigenvalues of matrix A. you must collect four linearly dependent solutions that are different. Note that a positive numbers square root should have both a - and + answer. Then determine the solution of the initial value problem where: [0 0 a' ¹ (0) = [8] (0) = z A₂ = 36 ₁ (t)= #₂(t)= =
Transcribed Image Text:Practice problem 21.6 You have been given the following second order linear system and its corresponding eigenvalues: 20 -16] A₁ = 4 -16 20 Guess a solution that has the form of: * = vewt And then substitute it in to z = Az Then guess what the values of v and w should be in relation to the eigenvectors and eigenvalues of matrix A. you must collect four linearly dependent solutions that are different. Note that a positive numbers square root should have both a - and + answer. Then determine the solution of the initial value problem where: [0 0 a' ¹ (0) = [8] (0) = z A₂ = 36 ₁ (t)= #₂(t)= =
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