that we should justify it today. However‚ treating slaves – most specifically slaves in the triangular trade – as property had economic impacts on areas such as Africa‚ West Europe‚ and the New World. The Triangular Trade was something that connected the three regions of North America and the Caribbean’s‚ Africa‚ and Europe. Today‚ we have international trade flows‚ inputs and outputs‚ and deals. The Triangular Trade was kind of like the 17th Century’s version of today’s trade system and “world order”
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About love Psychologists and researchers have proposed a number of different theories of love. Love is a basic human emotion‚ but understanding how and why it happens is not necessarily easy. In fact‚ for a long time‚ many people suggested that love was simply something that science couldn’t understand. The following are four of the major theories proposed to explain liking‚ love‚ and emotional attachment. Scales of Liking and Loving The nature of love has been explored by a number of theorists
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Fault-Tolerant Observers Supervisor: Dr Imad M. Jaimoukha Designing of a robust fault-tolerant observer that guarantees a certain level of performance for real-time applications. By: YEO Zhi-Wei‚ Laurence 00566245 Overview For any system such as a factory plant‚ an aircraft jet engine system or a water pumping system‚ it can be replicatedi by a mathematical model which includes the affecting dynamics based on observations and assumptions. However‚ it would be practically challenging
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Taare Zameen Par There is a scene in Taare Zameen Par when the protagonist Ishaan (Darsheel Safary) runs away from school and loiters on the road for the whole day – for the fear of being punished for not having done his homework. I never did anything like that in school but keep doing it regularly once I started work. The comparison might not be warranted but this is just one of those scenes which made me relate to Ishaan’s plight in the movie. On paper‚ this is the story of a kid suffering
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of linear algebra or matrix theory. The introduction and development of the notation of matrix and system of linear algebra followed the development of determinant‚ which rose from the study of coefficient system of linear equations. Leibnitz‚ one of the founders of calculus used determinant in 1693 an Cramer presented his determinant - based formula system of solving linear equations (known as Cramer’s’ rule) in 1750. In 1848‚ James J Sylvester introduced the term “matrix” which was Latin word
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Gaussian Elimination" (see Menu) Enter the matrix of coefficients and right-hand side vector You may edit the following statements or use the matrix and vector pallettes to enter new data ( see View‚ Palettes) > A:=<<4 | 2 | 3 | 2> ‚ <8 | 3 | -4 | 7> ‚ <4 | -6 | 2 | -5>>; > b:=<<15‚ 7‚ 6>>; Form the augmented matrix and solve The Maple routine GaussianElimination requires the augmented matrix A|b as input. In this worksheet this matrix is called Ab and is formed using <A|b> >
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Linear Least Squares Suppose we are given a set of data points {(xi ‚ fi )}‚ i = 1‚ . . . ‚ n. These could be measurements from an experiment or obtained simply by evaluating a function at some points. You have seen that we can interpolate these points‚ i.e.‚ either find a polynomial of degree ≤ (n − 1) which passes through all n points or we can use a continuous piecewise interpolant of the data which is usually a better approach. How‚ it might be the case that we know that these data points should
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.. 15 Matrices .................................................................................................................................................... 27 Matrix Arithmetic & Operations .............................................................................................................. 33 Properties of Matrix Arithmetic and the Transpose ................................................................................. 45 Inverse Matrices and Elementary Matrices ............
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1.1 SOLUTIONS Notes: The key exercises are 7 (or 11 or 12)‚ 19–22‚ and 25. For brevity‚ the symbols R1‚ R2‚…‚ stand for row 1 (or equation 1)‚ row 2 (or equation 2)‚ and so on. Additional notes are at the end of the section. 1. x1 + 5 x2 = 7 −2 x1 − 7 x2 = −5 1 −2 5 −7 7 −5 x1 + 5 x2 = 7 Replace R2 by R2 + (2)R1 and obtain: 3x2 = 9 x1 + 5 x2 = 7 x2 = 3 x1 1 0 1 0 1 0 5 3 5 1 0 1 7 9 7 3 −8 3 Scale R2 by 1/3: Replace R1 by R1
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Math 111 Homework 1 fall 2007 due 14/9 1. (1.2; 17) Determine the values of h such that the matrix is the augmented matrix of a system which admits a solution. 2 3 4 6 h 7 2. (1.2; 12) Find the general solutions of the system whose augmented matrix is 1 −7 0 6 5 0 0 1 −2 −3 −1 7 −4 2 7 1 −2 4 3. (1.3; 17) Let a1 = 4 ‚ a2 = −3 ‚ b = 1 . For what −2 7 h value(s) of h is b in the plane spanned by a1 and a2? 4. (1.4; 15) Let A = b1 2 −1 and b = . Show that the equation
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