Initialise Clear the workspace and load Linear Algebra package > restart; > with(LinearAlgebra): If you want practice at hand calculation you should use the worksheet "Interactive 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>>;
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have also learnt that a system of algebraic equations can be expressed in the form of matrices. This means‚ a system of linear equations like a1 x + b1 y = c 1 a2 x + b2 y = c 2 ⎡ a b ⎤ ⎡ x ⎤ ⎡c ⎤ can be represented as ⎢ 1 1 ⎥ ⎢ ⎥ = ⎢ 1 ⎥ . Now‚ this ⎣ a2 b2 ⎦ ⎣ y ⎦ ⎣ c2 ⎦ system of equations has a unique solution or not‚ is determined by the number a1 b2 – a2 b1. (Recall that if a1 b1 or‚ a1 b2 – a2 b1 ≠ 0‚ then the system of linear ≠ a2 b2 equations has a unique solution). The number a1 b2 –
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solution‚ x + s stand for the unknown plus standard‚ and Vt the total volume of solution‚ we can write Ax = ε bcxVx / Vt Ax + s = ε b(cxVx + csVs ) / Vt Dividing the first equation by the second and rearranging gives cx = Ax csVs 0.656 × 25.7 ×10.0 = = 21.1 ppm ( Ax + s − Ax )Vx (0.976 − 0.656) × 25.0 14-2. Using the equation developed in problem 14-1‚ we can write cCu 2+ = 0.723 × 2.75 × 1.00 = 2.0497 ppm (0.917 − 0.723) × 5.00 For dilute solutions‚ 1 ppm = 1 mg/L‚ so Percent Cu = 200 mL
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CIMA’S Official Study System Revised edition relevant for 2005/2006 Computer based assessment Certificate Level Business Mathematics Sandra Peers AMSTERDAM BOSTON HEIDELBERG PARIS SAN DIEGO SAN FRANCISCO LONDON NEW YORK SINGAPORE SYDNEY OXFORD TOKYO CIMA Publishing An imprint of Elsevier Linacre House‚ Jordan Hill‚ Oxford OX2 8DP 30 Corporate Drive‚ Burlington‚ MA 01803 First published 2005 Copyright # 2005‚ Elsevier Ltd. All rights reserved No part of this publication
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Licensed to: iChapters User Structural Analysis THIRD EDITION Aslam Kassimali Southern Illinois University—Carbondale Australia Canada Mexico Singapore Spain United Kingdom United States Copyright 2005 Cengage Learning‚ Inc. All Rights Reserved. May not be copied‚ scanned‚ or duplicated‚ in whole or in part. Licensed to: iChapters User Structural Analysis‚ Third Edition by Aslam Kassimali Associate Vice-President and Editorial Director:
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UTT MATH1002 Weeks 3&4 Notes Systems of ODEs First-order linear equations with constant coefficients [pic] [pic] Let [pic] [pic] Taking Laplace transforms of (1) and (2) [pic] [pic] From (3) and (4) [pic] [pic] We solve this system algebraically for [pic]and [pic] and obtain [pic] by taking inverse transforms. Example [pic] [pic] [pic] We have [pic] [pic] [pic] From (5) and (6) [pic] [pic] [pic]
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PARTIAL DIFFERENTIAL EQUATIONS I YEAR B.Tech By Mr. Y. Prabhaker Reddy Asst. Professor of Mathematics Guru Nanak Engineering College Ibrahimpatnam‚ Hyderabad. SYLLABUS OF MATHEMATICAL METHODS (as per JNTU Hyderabad) Name of the Unit Unit-I Solution of Linear systems Unit-II Eigen values and Eigen vectors Name of the Topic Matrices and Linear system of equations: Elementary row transformations – Rank – Echelon form‚ Normal form – Solution of Linear Systems – Direct Methods
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Linear ------------------------------------------------- Important EXERCISE 27 SIMPLE LINEAR REGRESSION STATISTICAL TECHNIQUE IN REVIEW Linear regression provides a means to estimate or predict the value of a dependent variable based on the value of one or more independent variables. The regression equation is a mathematical expression of a causal proposition emerging from a theoretical framework. The linkage between the theoretical statement and the equation is made prior to data collection
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Chapter 13 Linear Regression and Correlation True/False 1. If a scatter diagram shows very little scatter about a straight line drawn through the plots‚ it indicates a rather weak correlation. Answer: False Difficulty: Easy Goal: 1 2. A scatter diagram is a chart that portrays the correlation between a dependent variable and an independent variable. Answer: True Difficulty: Easy Goal: 1 AACSB: AS 3. An economist is interested in predicting
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DIFFERENTIAL EQUATIONS: A SIMPLIFIED APPROACH‚ 2nd Edition DIFFERENTIAL EQUATIONS PRIMER By: AUSTRIA‚ Gian Paulo A. ECE / 3‚ Mapúa Institute of Technology NOTE: THIS PRIMER IS SUBJECT TO COPYRIGHT. IT CANNOT BE REPRODUCED WITHOUT PRIOR PERMISSION FROM THE AUTHOR. DEFINITIONS / TERMINOLOGIES A differential equation is an equation which involves derivatives and is mathematical models which can be used to approximate real-world problems. It is a specialized area of differential calculus but it involves
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