describing the position of that point after a rotation. The product of two matrices is a matrix that represents the composition of two linear transformations. Another application of matrices is in the solution of a system of linear equations. If the matrix is square‚ it is possible to deduce some of its properties by computing its determinant. For example‚ a square matrix has an inverse if and only if its determinant is not zero. Eigenvalues and eigenvectors provide insight into the geometry of linear
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Introduction to Modern Algebra David Joyce Clark University Version 0.0.6‚ 3 Oct 2008 1 Copyright (C) 2008. 1 ii I dedicate this book to my friend and colleague Arthur Chou. Arthur encouraged me to write this book. I’m sorry that he did not live to see it finished. Contents 1 Introduction 1.1 Structures in Modern Algebra . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 Operations on sets . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.2 Fields . . . . .
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It is intended that by the end of this project‚ students will be able to: Understand the structure of exploration data files‚ Create‚ validate and composite a drillhole database‚ Build a block model‚ Estimate grades to blocks using Inverse Distance Technique‚ Generate the reserves‚ and Become familiar with an orebody modelling and resource estimation software package. The Deposit The deposit is a gold mineralisation which lies horizontally beneath the surface. A “first-pass”
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HPLC Determination of Aspartame in Diet Coke Name: xx Student Number: xxx Class: xxx Aim The aim of this experiment was to determine the concentration of aspartame in a sample of diet Coke® using HPLC as investigation tool. Introduction High Performance Liquid Chromatography (HPLC) is one of the most widely used analytical techniques of nonvolatile organic compounds. Chromatographic processes can be described
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and realism have‚ the two styles contrast a lot. Romanticism opposes earlier types of writing by digging into feeling‚ conviction‚ imagination‚ and dreams. It is a style that exploits the individual’s opportunity and spontaneity. Realism is on the inverse end of the spectrum‚ concentrating on points of interest trying to recreate this real world in a text form. The Raven and The Birth-Mark show romanticism while Huckleberry Finn shows the opposite with realism. First of all‚ individualism‚ as
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Macroeconomics Exam 1 Instructor: Prof. Phelps Name: Results: Class: Period: Date: Read each question carefully then circle the correct answer. When you are finished transfer the answers to the Scantron sheet. Make sure that you enter your name on both the exam and the scantron sheet. You have 1 hour to complete the exam. 1. For economists‚ the word "utility" means: a) versatility and flexibility. b) rationality. c) pleasure or satisfaction.** d) purposefulness
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following functions calculate the inverse of a matrix and saves it ## to the cache such that the next time the user attempts to calculate the ## matrix inverse‚ the previously saved value is returned instead of ## repeating the calculation. ## This function creates a special "matrix" object‚ which is really a list ## containing a function to ## 1. set the value of the matrix ## 2. get the value of the matrix ## 3. set the value of the inverse ## 4. get the value of the inverse makeCacheMatrix <- function(x
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determined by A and is called the inverse of A‚ denoted by A−1. It follows from the theory of matrices that if for finite square matrices A and B‚ then also [1] Non-square matrices (m-by-n matrices for which m ≠ n) do not have an inverse. However‚ in some cases such a matrix may have a left inverse or right inverse. If A is m-by-n and the rank of A is equal to n‚ then A has a left inverse: an n-by-m matrix B such that BA = I. If A has rank m‚ then it has a right inverse: an n-by-m matrix B such that
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ESSAY PLAN Title: Writing about design principles and analysis of image Introduction * Am discussing the aspects of visual composition in this first part of this essay * Basically‚ the next part is going to explain the use of design principles applied to the visual elements The Body * This will contain all the size variation that are used * The next thing is the visual effects Conclusion * Media is just a world on its own and by this means‚ big companies uses media to
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judgments about what the economy should be like or what particular policy action should be recommended‚ based on economic relationships. 5. Explain the terms ‘fallacy of composition’ and ‘the post-hoc fallacy’. Give examples. Why might these fallacies lead to wrong conclusions when analyzing economic problems? Fallacy of Composition refers to assuming that if one thing is true for a particular individual‚ it will also be true for a whole group. An example being that if one person states that they earn
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