Question: Consider the matrix 1 1 A = 1 0 Show that F Fa A: n+1 F, n-1 where n is a positive integer and

Consider the matrix 1 1 A = 1 0 Show that F

Consider the matrix 1 1 A = 1 0 Show that F Fa A": n+1 F, n-1 where n is a positive integer and F, is the nth Fibonacci number. Use this result to explain how you can calculate F, in O(log (n)) time.

Step by Step Solution

★★★★★

3.45 Rating (171 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Explain how you can impose your own limits on credit card spending.

Show that the following equivalences hold. Explain how you can apply then to improve the efficiency of certain queries: a. E 1 (E 2 E 3 ) = (E 1 E 2 E 1 E 3 ). b. (AG F (E)) = A G F ( ...

Explain how you can use slope to show that the points A(1, 5), B(3, 7), and C(5, 3) are the vertices of a right triangle.

Consider the matrix B = 23 13 13 13 2 3 13 13 13 2 3 (a) Show that B has eigenvalues ????1 = ????2 = 1 and ????3 = 0. (b) Find eigenvectors c1 for ????1 and c3 for ????3. Verify that these vectors...

Consider the function y = tanhx. a. By differentiating twice, show that y" = -2y + 2y 3 . b. Differentiate with respect to x up to y (5) and use this to determine the Maclaurin series of y = tanhx.

The Matrix for a Markov chain is (A) Show that R = [.4 0 .6] and S = [0 1 0] are both stationary matrices for P. Explain why this does not contradict Theorem 1 A. (B) Find another stationary matrix...

Consider the flow with velocity vector v = xi. Show that the individual particles have the position vectors r(t) = c1eti + c2j + c3k with constant c1, c2, c3. Show that the particles that at t = 0...

Consider the multiplicative model for a square table, a. Show that the model satisfies (i) symmetry, (ii) marginal homogeneity, (iii) quasi-symmetry, (iv) quasi-independence. b. Show that...

Consider the flow with velocity vector v = xi. Show that the individual particles have the position vectors r(t) = c 1 e t i + c 2 j + c 3 k with constant c 1 , c 2 , c 3 . Show that the particles...

Consider the differential equation 4xu + 2u + u = 0. Given that cos x solves the Given that cos x solves the boundary value problem u(1/4) 2 = 0, u( 2 ) = 1, and sin x solves the boundary value...

The table below shows the number of workers required to produce 1 unit of goods X and Y, for countries A and B. Country A Country B 1 unit of 8 workers 15 workers Good X 1 unit of 4 workers 5 workers...

Using the cognitive model and the BRUSO model discussed in class, write survey items for the following general questions. It may take more than one question. Responding to a survey item is itself a...

Read the following text carefully, then answer the question. Exciting New Gym Opening Soon!!! Northside Gym is opening soon, providing a new level of gym experience. The gym will meet all your...

Complete the self-scoring "Followership Questionnaire" in Ch. 13 (p. 487) of Leadership: Theory and Practice . DueThursday respond to the following: Based on your results from the "Followership...

Research by Ericsson and other suggests that about 10,000 hours of deliberate practice are required to become an expert. What is required for deliberate practice? Group of answer choices Focused...

International clothier Gap, Inc. is proud of its Code of Business Conduct that urges all those associated with the company to participate in "Doing the Right Thing." The business, founded in 1969,...

5 8 1 . The bank of tubes located at the back of the domestic refrigerators are the _ _ _ _ _ _ _ _ _ _ tubes. Refrigerant cooling Evaporator Condenser Throttling

Research corporate acquisitions using Web resources and then answer the following questions: Why do firms purchase other corporations? Do firms pay too much for the acquired corporation? Why do so...

In the past, some mutual funds often engaged in a practice called afterhours trading that allowed some of their larger shareholders to reap profits or avoid losses in a manner not available to all...

What is the intent of no fault insurance? How does no fault insurance generally work? What is a disadvantage of no fault insurance?

Name some ways an individual might handle a cash flow deficiency. Which way would be preferable? Why?

Why is the fund-raising ratio of key concern to both donors and nancial analysts?

What is the primary deciency of discrete presentation as it must be applied in government-wide statements?

Select the best answer. 1. Which of the following should not be included in the introductory section of a city's CAFR? a. Management's discussion and analysis b. Letter of transmittal c. Government...