Let A be a real 3 x 3 matrix, and assume that the linear system has a

Question:

Let A be a real 3 x 3 matrix, and assume that the linear system has a periodic solution of period P. Prove that every periodic solution of the system has period P. What other types of solutions can there be? Is the zero solution necessarily stable?

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Applied Linear Algebra

ISBN: 978-0131473829

1st edition

Authors: Peter J. Olver, Cheri Shakiban

See More Books

Question Posted: Jun 17, 2016 09:19 AM

See More Questions

Let A be a real 2 ( 2 matrix with complex eigenvalues = a ( bi such that b 0 and ( ( = 1. Prove that every trajectory of the dynamical system xk+1 = Axk lies on an ellipse. [Hint: Theorem 4.43...
Let A be a real n x n matrix, and let n x n be a vector in Cn. Show that Re(Ax) = A(Re x) and Im(Ax) = A(Im x).
Let A be a real 5 x 5 matrix, and assume that A has eigenvalues i, - i, -2, - 1 (and no others). Is the zero solution to the linear system u = A u necessarily stable? Explain. Does your answer change...
Establish procedures to guarantee substantiation of claims for allowances. Think about how you would set up a process to ensure employee claims and allowances could be claimed. Write a step by step...
In 2006, the Russ College of Engineering and Technology of Ohio University announced that an investigation had found rampant and flagrant plagiarism in the theses of mechanical engineering graduate...
The IASB exposure draft (ED) and re-exposure draft (RED) on revenue recognition discuss how onerous contracts should be reported and measured. Instructions Refer to the IASBs ED and RED "Revenue...
The listing of the ledger accounts (unadjusted) of New Systems Pty Ltd at 30 June 2025 is presented below. All ledger balances are normal balances. Additional information relating to the company is...
The 3M Company is a global diversified technology company active in the following product markets: consumer and office; display and graphics; electronics and communications; health care; industrial;...
Based on the data shown below, calculate the regression line (each value to two decimal places) y = x y 3 15.12 4 16.8 5 14.48 6 16.46 7 15.84 8 14.72 9 16.5 X +
The following table shows the percentage of on-time arrivals, the number of mishandled baggage reports per 1000 passengers, and the number of customer complaints per 1000 passengers for ten airlines...
(a) Show that the matrix has Î» = ± i as incomplete complex conjugate eigenvalues. (c) Explain the behavior of a typical solution. Why is the zero solution not stable? 0110 1001...
Are the conclusions of Exercise 9.2.8 valid when A is a 4 x 4 matrix?
A hand of 3 cards (without replacement) is chosen at random from an ordinary deck of 52 playing cards. (a) What is the probability that the hand contains only diamonds? (b) What is the probability...
Decide whether something is wrong with each of the graphs shown in Problems 13-17. Explain your reasoning. The graph shown in Figure 14.23 was circulated throughout the mathematics department of a...
What are two circumstances when the cost method is used for strategic investments?
A random variable has P (X = x) = x/15 for x = 1, 2, 3, 4, 5, and 0 otherwise. Find the mean and variance of X.
Madayag Development Corporation (MDC) is a real estate development company that is 60% owned by Thomas Madayag. Seatons Inc., a privately owned Canadian department store chain, owns 30%, and 10% is...
Explain the difference between user objectives and preparer objectives.
For the following exercises, rewrite the product as a sum or difference. 16sin(16x)sin(11x)
From 1970 to 1990, Sri Lanka's population grew by approximately 2.2 million persons every five years. The population in 1970 was 12.2 million people.What is the best formula for P, Sri Lanka's...
Use transformations to sketch the graph of the function. 11. y = -sin 2.x - sin 12. y = 3 In (x - 2) 13. y = (1 + e*)/2 14. y = 2- 15. f(x)= - {) if x <0 16. f(x) if x0
Determine whether f is even odd or neither even nor odd. (a) f (x) = 2x5 3x2 + 2 (b) f (x) = x3 x7 (c) f (x) = ex2 (d) f (x) = 1 + sin x
Find an expression for the function whose graph consists of the line segment from the point (2, 2) to the point (1, 0) together with the top half of the circle with center the origin and radius 1.
A pilot taxiing on the airport loses radio contact with ATC and then sees a flashing red light being shown at his aircraft from the Air Traffic Control Tower. What action should the pilot take?
Discussion questions: It is better to be a human being dissatisfied than a pig satisfied; better to be Socrates dissatisfied than a fool satisfied. 1. Do you agree? Why (not)? 2. What would a...
Describe how to make a strong magnet out of an initially unmagnetized iron rod without using the earth or another bar magnet. Include in your instructions the materials one would need, how one could...

Let A be a real 3 x 3 matrix, and assume that the linear system has a

Question:

ú = Au

Step by Step Answer:

Every solution to a real first order system of perio...View the full answer

Applied Linear Algebra

Students also viewed these Linear Algebra questions