Book edition 5th

Author(s) Otto Bretscher

Pages 442 pages

ISBN 9780321796974

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Short Answer

For the values of $λ_{1} = - 1$ and $λ_{1} = - 2$ , sketch the trajectories for all nine initial values shown in the following figures. For each of the points, trace out both future and past of the system.

The trajectories for all nine initial values is

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Draw the future and past of the system.

Consider the Eigen values $λ_{1} = - 1$ and $λ_{2} = - 2$ .

As 0 > $λ_{1} > λ_{2}$ , the future and past of the system toward outside.

Draw the graph of $E_{- 1}$ and $E_{- 2}$ as follows:

Step 2: Draw the trajectory of the system.

If the Eigen values of the system are $λ_{1}$ and $λ_{2}$ such that $λ_{1} > 0 > λ_{2}$ then the phase portraits of the system is

By the trajectory definition, draw the graph of the trajectory of the system as follows:

Hence the trajectories for all nine initial values and traces of the future and past of the system are sketched.

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Linear Algebra With Applications

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Short Answer

For the values of $λ_{1} = - 1$ and $λ_{1} = - 2$ , sketch the trajectories for all nine initial values shown in the following figures. For each of the points, trace out both future and past of the system.

Step by Step Solution

Step 1: Draw the future and past of the system.

Step 2: Draw the trajectory of the system.

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Linear Algebra With Applications

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Short Answer

For the values of λ1=-1 and λ1=-2 , sketch the trajectories for all nine initial values shown in the following figures. For each of the points, trace out both future and past of the system.

Step by Step Solution

Step 1: Draw the future and past of the system.

Step 2: Draw the trajectory of the system.

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For the values of $λ_{1} = - 1$ and $λ_{1} = - 2$ , sketch the trajectories for all nine initial values shown in the following figures. For each of the points, trace out both future and past of the system.