100 Note : Question no. one is compulsory. Attempt any three questions from four. 1. (a) For what value of ’k’ the points ( - k + 1‚ 2 k)‚ (k‚ 2 - 2 k) and ( - 4 - k‚ 6 - 2 k) are collinear. (b) Solve the following system of equations by using Matrix Inverse Method. 3x+ 4y+ 7z= 14 2x-y+ 3z= 4 2x + 2y - 3z = 0 (c) Use principle of Mathematical Induction to prove that : 1 ± 1 ± 1x2 2x3 (d) 1 n (n+1) n+1 5 5 5 5 -‚ How many terms of G.P ‚[3 3‚ 3 /3 Add upto 39 + 13 BCS-012 1 P.T.O
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All the Mathematics You Missed Beginning graduate students in mathematics and other quantitative subjects are expected to have a daunting breadth of mathematical knowledge‚ but few have such a background. This book will help students see the broad outline of mathematics and to fill in the gaps in their knowledge. The author explains the basic points and a few key results of the most important undergraduate topics in mathematics‚ emphasizing the intuitions behind the subject. The topics include linear
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of each column is unique 2. The value of each row is unique 3. The amount per square N * N is a unique internal[-http://www.cs.huji.ac.il] Percepts The Sudoku Game percepts are: 1-The field of Sudoku environment matrix is blank 2-The field of Sudoku environment matrix is not blank 3-The value of each filled row is unique 4-The value of each filled row is not unique 5-The value of each filled column is unique 6-The value of each filled column is not unique 7-The summation per each
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Adaptive Filters 1 Adaptive Filters A Tutorial for the Course Computational Intelligence http://www.igi.tugraz.at/lehre/CI Christian Feldbauer‚ Franz Pernkopf‚ and Erhard Rank Signal Processing and Speech Communication Laboratory Inffeldgasse 16c Abstract This tutorial introduces the LMS (least mean squares) and the RLS (recursive least-squares) algorithm for the design of adaptive transversal filters. These algorithms are applied for identification of an unknown system. Usage
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product developer that uses “the matrix” to set targets for their retail prices‚ that are usually 30-40% lower than its competitors (Moon‚ 2004). 2. What do you think of the company’s product strategy and product range? Do you agree with the matrix approach described in Figure B of the case? What is most important about IKEA’s product strategy and product range is their matrix‚ which is simple enough‚ yet very useful at creating market opportunities. The matrix also creates a way of accepting
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Guide Number (from tip) Distance from Tip (cm) 1 10 2 23 3 38 4 55 5 74 6 96 7 120 8 149 Define suitable variables and discuss parameters/constraints. Using Technology‚ pot the data points on a graph. Using matrix methods or otherwise‚ find a quadratic function and a cubic function which model this situation. Explain the process you used. On a new set of axes‚ draw these model functions and the original data points. Comment on any differences. Find a polynomial
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[edit]Linear independence As mentioned above‚ the determinant of a matrix (with real or complex entries‚ say) is zero if and only if the column vectors of the matrix are linearly dependent. Thus‚ determinants can be used to characterize linearly dependent vectors. For example‚ given two linearly independent vectors v1‚ v2 in R3‚ a third vector v3 lies in the plane spanned by the former two vectors exactly if the determinant of the 3 × 3 matrix consisting of the three vectors is zero. The same idea is also
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computations that are used in the PageRank algorithm. Some of the topics that we touch on include the following‚ but not limited to‚ are: linear algebra‚ node analysis‚ matrix theory‚ and numerical methods. But primarily this paper concerns itself with the use of the linear algebra involved in the computation of the Google matrix‚ which results in the Pagerank‚ which descibribes how important a page is. Importance is placed on the intuition of all related mathematical topics involved in the algorithm
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TYPES OF MOVIES Nearly one hundred years ago‚ human beings invented the gadget called camera. Nobody could have known the importance of this invention when it was devised. After years‚ television and cinema were invented‚ and people gradually understood the importance of these gadgets. They had a chance to join entertaining‚ interesting‚ and even amazing world of television and cinema because the life they saw in movies usually resembled their daily life. Now people have considered that movies
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MFE MATLAB Function Reference Financial Econometrics Kevin Sheppard October 30‚ 2009 2 c 2001-2009 Kevin Sheppard Contents Notes v 1 Included but not documented functions 1 2 Cross Sectional Analysis 5 2.1 Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.1 3 Regression: ols Stationary Time Series 3.1 ARMA Simulation . . . . . . . . . . .
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