Paper Assignment for Algebra Study Questions
Order ID 53563633773 Type Essay Writer Level Masters Style APA Sources/References 4 Perfect Number of Pages to Order 5-10 Pages Description/Paper Instructions
Paper Assignment – Algebra Study Questions
Mathematics 160.102 Algebra (Auckland, Manawatu, and Distance) MASSEY UNIVERSITY School of Fundamental Sciences and School of Natural and Computational Sciences
Due at 11 p.m., Assignment 2 Semester One, Tuesday, May 26, 2021
1. Given that z = 1 + 2i is a root of p(z) = z 4 5z 3 + 13z 2 19z + 10, determine all of p(zroots )’s and use them to represent p(z) as a product of (a) four linear factors and (b) real linear and real irreducible quadratic components. Use the command roots to check your roots in Matlab.
2. Plot the four roots of z 4 + z 2 + 1 in the complex plane using the subsitution w = z 2.
3. With n = 3, use de Moivre’s Theorem (ei) n = ein, or (cos+isin) n = cos(n)+isin(n), to get the triple angle formulae that represent sin(3), cos(3), and sin(3), respectively, in terms of sin() and cos().
4. Compute the determinant of 1 1 1 0 0 2 1 0 1 2 2 1 1 1 1 4 by using simple row operations (row echelon form).
In Matlab, verify your answer.
5. Prove that if is an eigenvalue of A, then 2 is an eigenvalue of A2 for all square matrices A.
6. Prove that if is an eigenvalue of A, then 1/ is an eigenvalue of A1 for all invertible square matrices A.
7. When Matlab is asked to supply the eigenvalues of a n n matrix (such as this one), what does it do?1 1 0 1 ) that has a smaller number of linearly independent eigenvectors than n? When a huge n n matrix has fewer than n linearly independent eigenvectors, how could you use Matlab to figure out? In Matlab, demonstrate your method.
8. The Matlab program randn(n) generates a nn matrix with each entry representing a random number from the normal distribution.
(a) Make a 4 4 matrix and find the eigenvalues and eigenvectors with Matlab.
Check in Matlab that the eigenvectors matrix may be used to diagonalize the matrix. How many eigenvalues are there in the real world? Do you always receive the same amount of real eigenvalues when you repeat the experiment with various random numbers?
(b) Make a big such matrix (without printing it; for example, use A = randn(100); where the semicolon prevents the result from being printed) and plot its eigenvalues as points in the complex plane. What do you think you’ve noticed? What happens if you change the value of n?
9. Even on a computer, computing the eigenvalues and eigenvectors for huge matrices the way we’ve been doing it by hand is too expensive. The power approach, which is faster, is as follows:
Step 1: Pick a nonzero x0 starting vector.
Step 2: For k = 0, 1, 2,…, let xk+1 = Axk
Step 3: For k = 0, 1, 2,…, let bk = x> k xk+1 x> k xk.
The sequence b0, b1, b2,… tends to the eigenvalue of A with the biggest modulus, and xk tends to an eigenvector. Let A = 3 1 1 12 0 5 4 2 1 and x0 = 1 1 1
Compute b0, b1, b2, b3, and b4 in Matlab.
How do they stack up against A’s biggest eigenvalue?
2
RUBRIC
QUALITY OF RESPONSE NO RESPONSE POOR / UNSATISFACTORY SATISFACTORY GOOD EXCELLENT Content (worth a maximum of 50% of the total points) Zero points: Student failed to submit the final paper. 20 points out of 50: The essay illustrates poor understanding of the relevant material by failing to address or incorrectly addressing the relevant content; failing to identify or inaccurately explaining/defining key concepts/ideas; ignoring or incorrectly explaining key points/claims and the reasoning behind them; and/or incorrectly or inappropriately using terminology; and elements of the response are lacking. 30 points out of 50: The essay illustrates a rudimentary understanding of the relevant material by mentioning but not full explaining the relevant content; identifying some of the key concepts/ideas though failing to fully or accurately explain many of them; using terminology, though sometimes inaccurately or inappropriately; and/or incorporating some key claims/points but failing to explain the reasoning behind them or doing so inaccurately. Elements of the required response may also be lacking. 40 points out of 50: The essay illustrates solid understanding of the relevant material by correctly addressing most of the relevant content; identifying and explaining most of the key concepts/ideas; using correct terminology; explaining the reasoning behind most of the key points/claims; and/or where necessary or useful, substantiating some points with accurate examples. The answer is complete. 50 points: The essay illustrates exemplary understanding of the relevant material by thoroughly and correctly addressing the relevant content; identifying and explaining all of the key concepts/ideas; using correct terminology explaining the reasoning behind key points/claims and substantiating, as necessary/useful, points with several accurate and illuminating examples. No aspects of the required answer are missing. Use of Sources (worth a maximum of 20% of the total points). Zero points: Student failed to include citations and/or references. Or the student failed to submit a final paper. 5 out 20 points: Sources are seldom cited to support statements and/or format of citations are not recognizable as APA 6th Edition format. There are major errors in the formation of the references and citations. And/or there is a major reliance on highly questionable. The Student fails to provide an adequate synthesis of research collected for the paper. 10 out 20 points: References to scholarly sources are occasionally given; many statements seem unsubstantiated. Frequent errors in APA 6th Edition format, leaving the reader confused about the source of the information. There are significant errors of the formation in the references and citations. And/or there is a significant use of highly questionable sources. 15 out 20 points: Credible Scholarly sources are used effectively support claims and are, for the most part, clear and fairly represented. APA 6th Edition is used with only a few minor errors. There are minor errors in reference and/or citations. And/or there is some use of questionable sources. 20 points: Credible scholarly sources are used to give compelling evidence to support claims and are clearly and fairly represented. APA 6th Edition format is used accurately and consistently. The student uses above the maximum required references in the development of the assignment. Grammar (worth maximum of 20% of total points) Zero points: Student failed to submit the final paper. 5 points out of 20: The paper does not communicate ideas/points clearly due to inappropriate use of terminology and vague language; thoughts and sentences are disjointed or incomprehensible; organization lacking; and/or numerous grammatical, spelling/punctuation errors 10 points out 20: The paper is often unclear and difficult to follow due to some inappropriate terminology and/or vague language; ideas may be fragmented, wandering and/or repetitive; poor organization; and/or some grammatical, spelling, punctuation errors 15 points out of 20: The paper is mostly clear as a result of appropriate use of terminology and minimal vagueness; no tangents and no repetition; fairly good organization; almost perfect grammar, spelling, punctuation, and word usage. 20 points: The paper is clear, concise, and a pleasure to read as a result of appropriate and precise use of terminology; total coherence of thoughts and presentation and logical organization; and the essay is error free. Structure of the Paper (worth 10% of total points) Zero points: Student failed to submit the final paper. 3 points out of 10: Student needs to develop better formatting skills. The paper omits significant structural elements required for and APA 6th edition paper. Formatting of the paper has major flaws. The paper does not conform to APA 6th edition requirements whatsoever. 5 points out of 10: Appearance of final paper demonstrates the student’s limited ability to format the paper. There are significant errors in formatting and/or the total omission of major components of an APA 6th edition paper. They can include the omission of the cover page, abstract, and page numbers. Additionally the page has major formatting issues with spacing or paragraph formation. Font size might not conform to size requirements. The student also significantly writes too large or too short of and paper 7 points out of 10: Research paper presents an above-average use of formatting skills. The paper has slight errors within the paper. This can include small errors or omissions with the cover page, abstract, page number, and headers. There could be also slight formatting issues with the document spacing or the font Additionally the paper might slightly exceed or undershoot the specific number of required written pages for the assignment. 10 points: Student provides a high-caliber, formatted paper. This includes an APA 6th edition cover page, abstract, page number, headers and is double spaced in 12’ Times Roman Font. Additionally, the paper conforms to the specific number of required written pages and neither goes over or under the specified length of the paper. GET THIS PROJECT NOW BY CLICKING ON THIS LINK TO PLACE THE ORDER
CLICK ON THE LINK HERE: https://www.perfectacademic.com/orders/ordernow
Also, you can place the order at www.collegepaper.us/orders/ordernow / www.phdwriters.us/orders/ordernow
Do You Have Any Other Essay/Assignment/Class Project/Homework Related to this? Click Here Now [CLICK ME]and Have It Done by Our PhD Qualified Writers!!