3. Consider the system of first order ODES (in matrix form)x-(::).3(a) Show thatt -x® (t) =t –(t) =et4t- 2is a set of fund ame nt al solutions of the system, for all real numbers t.(b) What type of equilibrium solution does this system have? Is the equilibrium solutionas ymptotically stable, neutrally stable or unst able?(c) Determine the fundamental matrix (t) which satisfies (0) =1 0%3D01

Given system x'=5-113x Let, A=5-113

Answered: 3. Consider the system of first order…

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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1 What is the solution for the following system of equations? 2x + y =77 X - 2y ='6 A (3, 1) (1, 3) C (-1, 4) (4, 1) E (4, -1)
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Consider the following. B = {(-2, -12, -6), (1, 4, 2), (3, 12, 7)}, B' = {(−1, 1, 3), (-2, 1, 3), (-2, 1, 4)}, [x] B¹ (a) Find the transition matrix from B to B'. P-1 = P = 2 (b) Find the transition matrix from B' to B. PP-1 = -26, 9, 27 -16, 5, 14 -10, -29 (c) Verify that the two transition matrices are inverses of each other. [x] B = ↓ 1 (d) Find the coordinate matrix [x]B, given the coordinate matrix [×]B'.
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