MA129 Mock Midterm Name: Time Allowed: 80 minutes Total Value: 40 marks Number of Pages: 8 Instructions: Non-programmable‚ non-graphing calculators are permitted. No other aids allowed. Check that your test paper has no missing‚ blank‚ or illegible pages. Note that test questions appear on both sides of the paper. Answer in the spaces provided. Show all your work. Insu¢ cient justi…cation will result in a loss of marks. 1. [3 marks] Let A = 2 1 4 1 3 2 ‚ B= 1 3 0 1
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Section 2.2 Matrices in Matlab 75 2.2 Matrices in Matlab You can think of a matrix as being made up of 1 or more row vectors of equal length. Equivalently‚ you can think of a matrix of being made up of 1 or more column vectors of equal length. Consider‚ for example‚ the matrix 1 2 3 0 A = 5 −1 0 0 . 3 −2 5 0 One could say that the matrix A is made up of 3 rows of length 4. Equivalently‚ one could say that matrix A is made up of 4 columns of length 3. In either model‚ we have 3 rows
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Exercise 4.1 2. Establish each of the following for all n ≥ 1 by the Principle of Mathematical Induction. Solution a) S(n): ==‚ S(1): = = =1‚ So S(1) is true. Assume S(k): = Consider S(k+1) = = +=-1+= -1. Hence‚ it follows that S(k)⇒S(k + 1) is true for all n ∈ Z+ by the Principle of Mathematical Induction. b) S( n) for n=1‚ = 2 = 2+(1-1). So S(1) is true. Inductive Step: assume S(k)is true‚ for some (particular) k ∈ Z+—that is‚ assume that =2+(k-1). For n=k+1‚ = + (k+1)
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Centre Number For Examiner’s Use Candidate Number Surname Other Names Examiner’s Initials Candidate Signature Question General Certificate of Education Advanced Subsidiary Examination January 2013 Mark 1 2 3 Mathematics MFP1 5 Unit Further Pure 1 Friday 18 January 2013 4 6 1.30 pm to 3.00 pm 7 For this paper you must have: * the blue AQA booklet of formulae and statistical tables. You may use a graphics calculator. 8 9 TOTAL Time
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1.1. Equations and Graphs In each of problems 1 - 4‚ find (a) an ordered pair that is a solution of the equation‚ (b) the intercepts of the graph‚ and (c) determine if the graph has symmetry. 1. 2. 3. 4. 5. Once a car is driven off of the dealership lot‚ it loses a significant amount of its resale value. The graph below shows the depreciated value of a BMW versus that of a Chevy after years. Which of the following statements is the best conclusion about the data? a. You should
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Texts Popular Music in America: The Beat Goes On‚ 4th ed. by Michael Campbell Schirmer‚ CENGAGE Learning. This book is available in hard copy from the boostore or as an ebook (6 months) from the publisher at its website: www.cengage.com/music/campbell. Whichever you purchase you must get the Digital Music Downloads Printed Access Card which gives you access to all the songs covered in the book.. The card‚ if ordered alone from the publisher‚ is: ISBN10:1-285-05737-6 or ISBN-13:
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IECON’01: The 27th Annual Conference of the IEEE Industrial Electronics Society SPACE VECTOR MODULATION –An Introduction == Tutorial at IECON2001== Dorin O. Neacsu Correspondence Address: Satcon Corporation‚ 161 First Street‚ Cambridge‚ MA 02142‚ Email neacsu@earthlink.net I. INTRODUCTION Space Vector Modulation became a standard for the switching power converters and important research effort has been dedicated to this topic. Tens of papers‚ research reports and patents were developed in the
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Mystery of ‘K’ in CMYK The K in CMYK stands for “Key”‚ but the answer is much more interesting than that. The “key plate” is said to add the “detail” to a printed image. This is true in that the black plate in a four color process print pushes the contrast and creates “detail”. Many people suggest that the theory of using K instead of B because it may be easily confused with “Blue” is a myth. While it is highly speculative what the reasoning is‚ there are context clues as to why it may actually
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University of Leicester MSc. in Risk‚ Crisis & Disaster Management Module 4 - Case Studies Essay "Given that disasters create opportunities for active learning - why do they repeat? Michael Lübke Student No.: 109023384 Intake: September 2010 MODULE 4 - CASE STUDIES !1 MICHAEL LÜBKE Institute of Lifelong Learning University of Leicester Plagiarism Declaration This form must be completed‚ signed and submitted with each assessment
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Universidad Autónoma de Querétaro Facultad de Ingeniería “Iterative Methods” “Gauss and Gauss-Seidel” Profesor | | Nieves Fonseca Ricardo | Mentado Camacho Félix Navarro Escamilla Erandy Péloquin Blancas María José Rubio Miranda Ana Luisa Abstract Many real life problems give us several simultaneous linear equations to solve. And we have to find a common solution for each of them. There are several techniques to use. Instead of using methods that provide a solution to a set
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