Differential Equations and Linear Algebra (4th Edition)
4th Edition
ISBN: 9780321964670
Author: Stephen W. Goode, Scott A. Annin
Publisher: PEARSON
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Textbook Question
Chapter 9.10, Problem 5P
Problems
For Problems 1-9, determine all equilibrium points of the given system and, if possible, characterize them as centers, spirals, saddles, or nodes.
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Question 1. Solve the system
-
x1 x2 + 3x3 + 2x4
-x1 + x22x3 + x4
2x12x2+7x3+7x4
Question 2. Consider the system
= 1
=-2
= 1
3x1 - x2 + ax3
= 1
x1 + 3x2 + 2x3
x12x2+2x3
= -b
= 4
1 For what values of a, b will the system be inconsistent?
2 For what values of a, b will the system have only one solution?
For what values of a, b will the saystem have infinitely many solutions?
Chapter 9 Solutions
Differential Equations and Linear Algebra (4th Edition)
Ch. 9.1 - For Question a-j, decide if the given statement is...Ch. 9.1 - For Question a-j, decide if the given statement is...Ch. 9.1 - For Question a-j, decide if the given statement is...Ch. 9.1 - For Question a-j, decide if the given statement is...Ch. 9.1 - Prob. 5TFRCh. 9.1 - For Question a-j, decide if the given statement is...Ch. 9.1 - Prob. 7TFRCh. 9.1 - For Question a-j, decide if the given statement is...Ch. 9.1 - Prob. 9TFRCh. 9.1 - Prob. 10TFR
Ch. 9.1 - Problems For problems 1-8, solve the given system...Ch. 9.1 - Problems For problems 1-8, solve the given system...Ch. 9.1 - Problems For problems 1-8, solve the given system...Ch. 9.1 - Prob. 4PCh. 9.1 - Problems For problems 1-8, solve the given system...Ch. 9.1 - Prob. 6PCh. 9.1 - Problems For problems 1-8, solve the given system...Ch. 9.1 - Problems For problems 1-8, solve the given system...Ch. 9.1 - Problems For Problems 9-11, solve the given...Ch. 9.1 - Problems For Problem 9-11, solve the given...Ch. 9.1 - Problems For Problem 9-11, solve the given...Ch. 9.1 - Problems For Problems 12-14, solve the given...Ch. 9.1 - Problems For Problems 12-14, solve the given...Ch. 9.1 - Prob. 14PCh. 9.1 - Problems For Problem 15-16, convert the given...Ch. 9.1 - Problems For Problem 15-16, convert the given...Ch. 9.1 - Prob. 17PCh. 9.1 - For Problems 17-19, convert the given linear...Ch. 9.1 - Prob. 19PCh. 9.1 - Prob. 20PCh. 9.1 - Solve the initial-value problem:...Ch. 9.2 - Prob. 1TFRCh. 9.2 - True-False Review For Questions a-g, decide if the...Ch. 9.2 - Prob. 3TFRCh. 9.2 - True-False Review For Questions a-g, decide if the...Ch. 9.2 - Prob. 5TFRCh. 9.2 - Prob. 6TFRCh. 9.2 - Prob. 7TFRCh. 9.2 - Problems
For Problems 1-5, show that the given...Ch. 9.2 - Problems
For Problems 1-5, show that the given...Ch. 9.2 - Problems
For Problems 1-5, show that the given...Ch. 9.2 - Problems
For Problems 1-5, show that the given...Ch. 9.2 - Problems
For Problems 1-5, show that the given...Ch. 9.2 - Problems
For Problems 6-9, show that the given...Ch. 9.2 - Problems
For Problems 6-9, show that the given...Ch. 9.2 - Problems
For Problems 6-9, show that the given...Ch. 9.2 - Problems
For Problems 6-9, show that the given...Ch. 9.2 - Prove that Vn(I) is a vector space.Ch. 9.2 - Problems
Let A(t) be an nn matrix function....Ch. 9.2 - If A=[2413], determine two linearly independent...Ch. 9.2 - Consider the differential equation...Ch. 9.3 - True-False Review For Questions a-d, decide if the...Ch. 9.3 - Prob. 2TFRCh. 9.3 - Prob. 3TFRCh. 9.3 - Prob. 4TFRCh. 9.3 - For Problems 1-7, show that the given functions...Ch. 9.3 - For Problems 1-7, show that the given functions...Ch. 9.3 - For Problems 17, show that the given function are...Ch. 9.3 - For Problems 1-7, show that the given functions...Ch. 9.3 - For Problems 1-7, show that the given functions...Ch. 9.3 - For Problems 1-7, show that the given functions...Ch. 9.3 - For Problems 1-7, show that the given functions...Ch. 9.3 - Prob. 8PCh. 9.3 - Prob. 9PCh. 9.4 - For Problems 116, determine the general solution...Ch. 9.4 - For Problems 116, determine the general solution...Ch. 9.4 - For Problems 116, determine the general solution...Ch. 9.4 - For Problems 116, determine the general solution...Ch. 9.4 - For Problems 116, determine the general solution...Ch. 9.4 - For Problems 116, determine the general solution...Ch. 9.4 - For Problems 116, determine the general solution...Ch. 9.4 - For Problems 116, determine the general solution...Ch. 9.4 - For Problems 116, determine the general solution...Ch. 9.4 - For Problems 116, determine the general solution...Ch. 9.4 - For Problems 1-16, determine the general solution...Ch. 9.4 - For Problems 1-16, determine the general solution...Ch. 9.4 - For Problems 1-16, determine the general solution...Ch. 9.4 - For Problems 1-16, determine the general solution...Ch. 9.4 - For Problems 1-16, determine the general solution...Ch. 9.4 - For Problems 1719, solve the initial-value problem...Ch. 9.4 - Prob. 18PCh. 9.4 - For Problems 1719, solve the initial-value problem...Ch. 9.4 - Prob. 20PCh. 9.4 - Consider the differential equation...Ch. 9.4 - Prob. 22PCh. 9.4 - Prob. 23PCh. 9.4 - Let A be a 22 nondefective matrix. If every...Ch. 9.4 - Prob. 25PCh. 9.4 - Prob. 26PCh. 9.4 - Prob. 27PCh. 9.4 - The motion of a certain physical system is...Ch. 9.5 - True-False Review For Questions a-d, decide if the...Ch. 9.5 - Prob. 2TFRCh. 9.5 - True-False Review For Questions a-d, decide if the...Ch. 9.5 - Prob. 4TFRCh. 9.5 - For Problem 114, determine the general solution to...Ch. 9.5 - For Problem 114, determine the general solution to...Ch. 9.5 - For Problem 114, determine the general solution to...Ch. 9.5 - For Problem 114, determine the general solution to...Ch. 9.5 - For Problem 114, determine the general solution to...Ch. 9.5 - For Problem 114, determine the general solution to...Ch. 9.5 - For Problem 114, determine the general solution to...Ch. 9.5 - For Problem 114, determine the general solution to...Ch. 9.5 - For Problem 114, determine the general solution to...Ch. 9.5 - For Problem 114, determine the general solution to...Ch. 9.5 - For Problem 114, determine the general solution to...Ch. 9.5 - Prob. 12PCh. 9.5 - Prob. 14PCh. 9.5 - For Problem 1516, solve the initial-value problem....Ch. 9.5 - For Problem 1516, solve the initial-value problem....Ch. 9.5 - Show that if the vector differential equation x=Ax...Ch. 9.5 - Prob. 18PCh. 9.5 - Prob. 19PCh. 9.5 - Prob. 20PCh. 9.6 - True-False Review For Questions (a)(f), decide if...Ch. 9.6 - Prob. 2TFRCh. 9.6 - Prob. 3TFRCh. 9.6 - Prob. 4TFRCh. 9.6 - True-False Review For Questions (a)(f), decide if...Ch. 9.6 - Prob. 6TFRCh. 9.6 - Problems For Problems 19, use the variation of...Ch. 9.6 - Problems For Problems 19, use the variation of...Ch. 9.6 - Problems For Problems 19, use the variation of...Ch. 9.6 - Problems For Problems 19, use the variation of...Ch. 9.6 - Problems For Problems 19, use the variation of...Ch. 9.6 - Problems For Problems 19, use the variation of...Ch. 9.6 - Problems For Problems 19, use the variation of...Ch. 9.6 - Problems For Problems 19, use the variation of...Ch. 9.6 - Problems Let X(t) be a fundamental matric for the...Ch. 9.6 - Problems Consider the nonhomogeneous system...Ch. 9.7 - True-False Review For Questions a-e, decide if the...Ch. 9.7 - Prob. 2TFRCh. 9.7 - True-False Review For Questions a-e, decide if the...Ch. 9.7 - Prob. 4TFRCh. 9.7 - True-False Review For Questions a-e, decide if the...Ch. 9.7 - Derive the eigenvalues and eigenvectors given in...Ch. 9.7 - Prob. 2PCh. 9.7 - Prob. 3PCh. 9.7 - Determine the general motion of the coupled...Ch. 9.7 - Prob. 5PCh. 9.7 - Prob. 6PCh. 9.7 - Prob. 7PCh. 9.7 - Prob. 8PCh. 9.7 - Prob. 9PCh. 9.7 - Prob. 11PCh. 9.8 - Prob. 1TFRCh. 9.8 - Prob. 2TFRCh. 9.8 - Prob. 3TFRCh. 9.8 - Prob. 4TFRCh. 9.8 - Prob. 5TFRCh. 9.8 - Prob. 6TFRCh. 9.8 - Prob. 1PCh. 9.8 - Prob. 2PCh. 9.8 - Prob. 3PCh. 9.8 - Prob. 4PCh. 9.8 - Prob. 5PCh. 9.8 - Prob. 8PCh. 9.8 - Prob. 9PCh. 9.8 - Prob. 10PCh. 9.8 - Prob. 11PCh. 9.9 - True-False Review For Questions a-f, decide if the...Ch. 9.9 - True-False Review For Questions a-f, decide if the...Ch. 9.9 - Prob. 3TFRCh. 9.9 - Prob. 4TFRCh. 9.9 - Prob. 5TFRCh. 9.9 - Prob. 6TFRCh. 9.9 - Prob. 1PCh. 9.9 - Prob. 2PCh. 9.9 - Prob. 3PCh. 9.9 - Prob. 4PCh. 9.9 - Prob. 5PCh. 9.9 - Prob. 6PCh. 9.9 - Prob. 7PCh. 9.9 - Prob. 8PCh. 9.9 - For Problems 5-20, characterize the equilibrium...Ch. 9.9 - Prob. 10PCh. 9.9 - Prob. 11PCh. 9.9 - Prob. 12PCh. 9.9 - Prob. 13PCh. 9.9 - Prob. 14PCh. 9.9 - For Problems 5-20, characterize the equilibrium...Ch. 9.9 - Prob. 16PCh. 9.9 - For Problems 5-20, characterize the equilibrium...Ch. 9.9 - For Problems 5-20, characterize the equilibrium...Ch. 9.9 - For Problems 5-20, characterize the equilibrium...Ch. 9.9 - Prob. 20PCh. 9.9 - Prob. 21PCh. 9.9 - Prob. 22PCh. 9.9 - For Problems 22-25, convert the given differential...Ch. 9.9 - Prob. 26PCh. 9.9 - Prob. 27PCh. 9.10 - For Questions a-e, decide if the given statement...Ch. 9.10 - Prob. 1PCh. 9.10 - Prob. 2PCh. 9.10 - Prob. 3PCh. 9.10 - Problems For Problems 1-9, determine all...Ch. 9.10 - Problems For Problems 1-9, determine all...Ch. 9.10 - Problems For Problems 1-9, determine all...Ch. 9.10 - Prob. 7PCh. 9.10 - Prob. 8PCh. 9.10 - Prob. 9PCh. 9.10 - Prob. 10PCh. 9.10 - Prob. 11PCh. 9.10 - Prob. 12PCh. 9.10 - Prob. 13PCh. 9.10 - Prob. 14PCh. 9.10 - Prob. 15PCh. 9.10 - Prob. 16PCh. 9.10 - Problem For Problems 13-18, sketch the phase...Ch. 9.10 - Prob. 18PCh. 9.10 - Prob. 19PCh. 9.10 - Prob. 20PCh. 9.10 - Problems Consider the differential equation...Ch. 9.11 - Additional Problems Verify that x1(t)=[et2t1] and...Ch. 9.11 - Prob. 2APCh. 9.11 - Prob. 3APCh. 9.11 - Prob. 4APCh. 9.11 - Prob. 5APCh. 9.11 - Prob. 6APCh. 9.11 - Prob. 7APCh. 9.11 - Prob. 8APCh. 9.11 - Additional Problems For Problems 3-24, determine...Ch. 9.11 - ADDITIONAL PROBLEMS For Problems 3-24, determine...Ch. 9.11 - Prob. 11APCh. 9.11 - Prob. 12APCh. 9.11 - Prob. 13APCh. 9.11 - Prob. 14APCh. 9.11 - For Problems 324, determine the general solution...Ch. 9.11 - Prob. 16APCh. 9.11 - Prob. 17APCh. 9.11 - Prob. 18APCh. 9.11 - Prob. 19APCh. 9.11 - Prob. 20APCh. 9.11 - Prob. 21APCh. 9.11 - Prob. 22APCh. 9.11 - Prob. 23APCh. 9.11 - Prob. 24APCh. 9.11 - Prob. 25APCh. 9.11 - For Problems 2529, use the variation-of-parameters...Ch. 9.11 - For Problems 2529, use the variation-of-parameters...Ch. 9.11 - Prob. 28APCh. 9.11 - Prob. 29APCh. 9.11 - True or False: If X(t) is a fundamental matrix for...Ch. 9.11 - Prob. 31APCh. 9.11 - Prob. 32APCh. 9.11 - Consider the differential equation...Ch. 9.11 - Prob. 34APCh. 9.11 - For Problems 34-41, characterize the equilibrium...Ch. 9.11 - Prob. 36APCh. 9.11 - Prob. 37APCh. 9.11 - Prob. 38APCh. 9.11 - Prob. 39APCh. 9.11 - Prob. 40APCh. 9.11 - Prob. 41APCh. 9.11 - Prob. 42APCh. 9.11 - Prob. 43AP
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