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Get Full Access to Linear Algebra And Its Applications - 5 Edition - Chapter 5.7 - Problem 11e
Get Full Access to Linear Algebra And Its Applications - 5 Edition - Chapter 5.7 - Problem 11e

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# Solution: In Exercises 9–18, construct the general solution

ISBN: 9780321982384 49

## Solution for problem 11E Chapter 5.7

Linear Algebra and Its Applications | 5th Edition

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Problem 11E

Problem 11E

In Exercises 9–18, construct the general solution of  involving complex eigenfunctions and then obtain the general real solution. Describe the shapes of typical trajectories.

Step-by-Step Solution:

Solution  11E

Step 1 of 7

Consider the matrix differential equation:

, where.

The objective is to find the general solution of the differential equation.

Find the eigenvalues of the matrix :

The characteristic polynomial is,

The roots of the characteristic equation are, .

Step 2 of 7

Step 3 of 7

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Solution: In Exercises 9–18, construct the general solution