There are questions related to some of your resource ID cards that have generated values of the parameters P, Q, R, S, T leading to singular matrices. Should you have these situations please do as instructed below:
In YOUR cw submission please do these: (1) say why your original id code does not give you an answer and (2) select different values for one/two of your parameters and listed the values you have chosen clearly in your work before you write your answers.
1 MATH1180 2021/22 Computational Methods and Numerical Techniques Main Cycle Coursework 1 INDIVIDUAL COURSEWORK Contribution: 25% of the module Module leader: Prof. Choi-Hong Lai Banner Assessment CRN 12952 No. 27550 (This information is not for students.) Submission deadline: Thursday 09/12/2021 This coursework should take an average student who is up-to-date with lectures and tutorials approximately 15 hours. Assessing Learning Outcomes 1, 2 and 3 ONLY: 1 Demonstrate knowledge of key techniques in linear algebra and calculus. 2 Understand concepts and structures in linear algebra and how to apply them to a range of problems. 3 Understand concepts and structures in multivariable calculus and how to apply them to a range of problems. Plagiarism is presenting somebody else's work as your own. It includes: copying information directly from the Web or books without referencing the material; submitting joint coursework as an individual effort; copying another student's coursework; stealing coursework from another student and submitting it as your own work. Suspected plagiarism will be investigated and if found to have occurred will be dealt with according to the procedures set down by the University. Please see your student handbook for further details of what is / isn't plagiarism. All material copied or amended from any source (e.g. internet, books) must be referenced correctly according to the reference style you are using. Coursework Submission Requirements • An ELECTRONIC copy of your coursework should be fully uploaded on or before Thursday 09/12/2021 23:30 using the link for Coursework 1 on the Moodle page for MATH1180. • You MUST ONLY submit a SINGLE PDF document. • Hand-written work is encouraged, but when scanning do ensure the file size is not excessive. • There are limits on the file size (see the relevant course Moodle page). • Make sure that any files you upload are virus-free and not protected by a password or corrupted otherwise they will be treated as null submissions. • Your work will not be printed in colour. Please ensure that any pages with colour are acceptable when printed in Black and White. • You must NOT submit a paper copy of this coursework. • All coursework must be submitted as above. Under no circumstances can they be accepted by academic staff. 2 The University website has details of the current Coursework Regulations, including details of penalties for late submission, procedures for Extenuating Circumstances, and penalties for Assessment Offences. See https://www.gre.ac.uk/student-services/regulations-and-policies. Coursework Specification See below for detailed specification. Deliverables CRN 12952 No. 27550 (25% of the module) Individual Coursework Deliverable: Your own work in a single pdf file that includes all the working out and answers for the questions in the following coursework specification. Grading Criteria Grades can be easily worked out by observing the marks allocated for each part of the coursework. An excellent coursework is one that is complete, has few errors and includes working and therefore will receive a mark in excess of 70%. A coursework that is just a pass at 40% will have multiple errors, working missing and possibly even questions missing. To be certain of getting the best mark include all working and attempt all questions. Assessment Criteria The marks allocated per section of the coursework are identified in brackets by the side of a question. You will be assessed on the correctness and completeness of the coursework. Grade % 70-100 The coursework is excellent/outstanding and is evidence of comprehensive knowledge, understanding and skills appropriate to the level of this module. There is also excellent evidence showing that all the learning outcomes and responsibilities appropriate to that level are satisfied. 60-69 The coursework is very good and is evidence of the knowledge, understanding and skills appropriate to the level of this course. There is also good evidence showing that all the learning outcomes and responsibilities appropriate to that level are satisfied. 50-59 The coursework is sound and provides some evidence of the knowledge, understanding and skills appropriate to the level of this module. There is also certain evidence showing that most of the learning outcomes and responsibilities to that level are satisfied. 40-49 The coursework is acceptable but provides restricted evidence of the knowledge, understanding and skills appropriate to the level of this module. There is also acceptable but restricted evidence showing that all the learning outcomes and responsibilities appropriate to that level are satisfied. 0-39 The coursework provides insufficient evidence of the knowledge, understanding and skills appropriate to the level of this module. The evidence provided shows many of the learning outcomes and responsibilities appropriate to this module are unsatisfied. https://www.gre.ac.uk/student-services/regulations-and-policies 3 Answer all questions, working needs to be shown to get full marks. At the front page of your submission write down your banner student id., starting with 000 or 001. For example: 0 0 0/1 9 0 2 4 8 2 Ignore the first three digits, and replace any remaining 0’s by 7’s. i.e., 9 7 2 4 8 2 Order your id. from SMALLEST to LARGEST. i.e., 2 2 4 7 8 9 • Label the values ??, ??, ??, ??, ??, ?? as shown: P Q R S T U • Make sure you WRITE DOWN the values of ??, ??, ??, ??, ??, ??, for your student id. on the FRONT COVER of the coursework submission. • Use the values for ??, ??, ??, ??, ??, ?? in the following questions where applicable as constants. 4 Q1 Use these matrices and vectors for Q1 ONLY: ?? = �?? ???? ??�, ?? = � 0 −1 ?? ?? �, and ?? = �?? 00 −??�, and the vector ?? = � ?? ??�. Let ?? be the 2 × 2 identity matrix. (i) Find ??−1. (ii) Using the inverse obtained in (i) find ?? in the linear system of equations ???? = ??. (iii) Find the eigenvalues of ?? and the corresponding eigenvectors. (iv) Without perform any calculation find the eigenvalues of ?? and explain why. Find also the corresponding eigenvectors. (v) Explain what happen when ?? is applied to its eigenvectors. [8 marks each = 40 marks] Q2 Evaluate the double integral ∬ (??3 + 2??)????????Ω over the region Ω given as in the diagram below. (You need to work out the limits of the double integral first.) [20 marks] (3,0) (3,36) ?? = 4??2 Ω 5 Q3 Let ?? = � ?? ?? ?? �, ?? = � ?? ?? ?? � and ?? = � 1 1 ?? �. (i) Calculate the angle between the two vectors ?? and ??. [5 marks] (ii) Find the value of ?? such that ?? and ?? are orthogonal. [5 marks] (iii) Find the value of ?? such that ??, ??, ?? are linearly dependent. [15 marks] (iv) Using the result in (iii) choose a value of ?? such that ??, ??, ?? are linearly independent and obtain a basis for the three-dimensional space ℝ3 using Gaussian Elimination Method. (Marks will be awarded only with Gaussian Elimination Method) [15 marks] Coursework Submission Requirements An ELECTRONIC copy of your coursework should be fully uploaded on or before Thursday 09/12/2021 23:30 using the link for Coursework 1 on the Moodle page for MATH1180. You MUST ONLY submit a SINGLE PDF document. There are limits on the file size (see the relevant course Moodle page). Make sure that any files you upload are virus-free and not protected by a password or corrupted otherwise they will be treated as null submissions. You must NOT submit a paper copy of this coursework. All coursework must be submitted as above. Under no circumstances can they be accepted by academic staff. The University website has details of the current Coursework Regulations, including details of penalties for late submission, procedures for Extenuating Circumstances, and penalties for Assessment Offences. See https://www.gre.ac.uk/student-services/...