Differential Equations: An Introduction to Modern Methods and Applications

3rd Edition

ISBN: 9781118531778

Author: James R. Brannan, William E. Boyce

Publisher: WILEY

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Textbook Question

Chapter 3.1, Problem 20P

Eigenvalues and Eigenvectors. In each of Problems 13 through 32 , find the eigenvalues and eigenvectors of the given matrix.

A = ( 2 − 1 3 − 2 )

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Chapter 3.1, Problem 19P

Chapter 3.1, Problem 21P

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2. Consider the following statement: For each natural number n, (3.2n+2.3n+1) is a prime number. (a) Explore this statement by completing the table below for n = 2,3 and two additional values of n of your choosing (notice n = 1 has been completed for you). One of your rows should contain a counterexample. n 1 3.2 2.3 +1 3.212.31 + 1 = 13 prime or composite? prime 2 3 (b) Write a formal counterexample argument for the statement using the template from

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Differential Equations: An Introduction to Modern Methods and Applications

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Eigenvalues and Eigenvectors. In each of Problems 13 through 32 , find the eigenvalues and eigenvectors of the given matrix. A = ( 2 − 1 3 − 2 )

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