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Consider the linear system y' (t) = Ay(t) where the real matrix A has an [2²4] · eigenvalue X = −1+i with associated eigenvector v = [y₁ (t)] Assume your real solution is in the form (t)e where

Consider the linear system y' (t) = Ay(t) where the real matrix A has an [2²4] · eigenvalue X = −1+i with associated eigenvector v = [y₁ (t)] Assume your real solution is in the form (t)e where

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...
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The options for matching the values of c1 and c2 are -4 through 1.

Consider the linear system y' (t) = Ay(t) where the real matrix A has an [2²4] eigenvalue X = −1+i with associated eigenvector v = Assume your real solution is in the form cos(t) 2 cos(t) + sin(t) Match a and b to the correct values a = [c1] and b = [c2]. y(t) = e-t =e-¹ [20 y₁ (t)] Y₂ (t). = (t)c where a sin(t) (bcos(t)) + 2 sin(t). 6)].
Transcribed Image Text:Consider the linear system y' (t) = Ay(t) where the real matrix A has an [2²4] eigenvalue X = −1+i with associated eigenvector v = Assume your real solution is in the form cos(t) 2 cos(t) + sin(t) Match a and b to the correct values a = [c1] and b = [c2]. y(t) = e-t =e-¹ [20 y₁ (t)] Y₂ (t). = (t)c where a sin(t) (bcos(t)) + 2 sin(t). 6)].
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