2. Let A be a constant 2 × 2 matrix.(a) Let ø(t) and x(t) be solutions of the initial value problem r'Ar,z(0) = (1).Show that the linear combination n(t) = ø(t) +x(t) is nota solution of this initial value problem.(b) Let ø(t) and x(t) be solutions of the inhomogeneous linear system r'Ax +Show that the linear combination n(t) = ø(t) + x(t) is not12a solution of this system.

Note: According to bartleby guidelines; for more than one question asked, only the first one is to…

2. Let A be a constant 2 x 2 matrix. (a) Let ø(t) and x(t) be solutions of the initial value problem r' Ar, z(0) = (;). Show that the linear combination n(t) = o(t) + x(t) is not a solution of this initial value problem.

2. Let A be a constant 2 x 2 matrix. (a) Let ø(t) and x(t) be solutions of the initial value problem r' Ar, z(0) = (;). Show that the linear combination n(t) = o(t) + x(t) is not a solution of this initial value problem.

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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Differential Equations

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Question

2. Let A be a constant 2 × 2 matrix.
(a) Let ø(t) and x(t) be solutions of the initial value problem r'
Ar,
z(0) = (1).
Show that the linear combination n(t) = ø(t) +x(t) is not
a solution of this initial value problem.
(b) Let ø(t) and x(t) be solutions of the inhomogeneous linear system r'
Ax +
Show that the linear combination n(t) = ø(t) + x(t) is not
12
a solution of this system.

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