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It is known that a real matrix A has eigenvalues A₁ = 2 and A₂ = 1 + 2i with corresponding eigenvectors and x(t) solves x' (t) = Ax(t) with initial conditions V1 V2 = 1 0 1 [1+3i] x(0) = -8 0 a. Find an expression for x(1). Give the answer in real form (no complex numbers or complex exponentials).

It is known that a real matrix A has eigenvalues A₁ = 2 and A₂ = 1 + 2i with corresponding eigenvectors and x(t) solves x' (t) = Ax(t) with initial conditions V1 V2 = 1 0 1 [1+3i] x(0) = -8 0 a. Find an expression for x(1). Give the answer in real form (no complex numbers or complex exponentials).

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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It is known that a real matrix A has eigenvalues A₁ = 2 and A₂ = 1 + 22 with corresponding eigenvectors 4 and x(t) solves x' (t) = Ax(t) with initial conditions V₁1 = 1 0 --E V2 = 1 1+ 3i x(0) = a. Find an expression for x(1). Give the answer in real form (no complex numbers or complex exponentials).
Transcribed Image Text:It is known that a real matrix A has eigenvalues A₁ = 2 and A₂ = 1 + 22 with corresponding eigenvectors 4 and x(t) solves x' (t) = Ax(t) with initial conditions V₁1 = 1 0 --E V2 = 1 1+ 3i x(0) = a. Find an expression for x(1). Give the answer in real form (no complex numbers or complex exponentials).
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