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erg2018assign1 - analysis states that the total output is...

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The Chinese University of Hong Kong Department of Systems Engineering & Engineering Management ERG 2018 Advanced Engineering Mathematics (2008) Assignment 1 Question 1 Solve the following 3 problems in your textbook (Kolman & Hill, 2008): (a) Section 1.1, Q.20 and Q.21 (b) Section 1.2, Q.19 (c) Section 1.3, Q.49 Question 2 Solve the following 3 linear equations 3 x 1 - 0 . 1 x 2 - 0 . 2 x 3 = 7 . 85 0 . 1 x 1 + 7 x 2 - 0 . 3 x 3 = - 19 . 3 0 . 3 x 1 - 0 . 2 x 2 + 10 x 3 = 71 . 4 (a) Using Cramer’s rule (b) Using Gauss elimination (c) Using Gauss-Jordan method Question 3 For solving Ax = y , Gauss elimination uses forward elimination to reduce [ A | y ] to [ U | z ] and then applies back-substitution to obtain x . Consider an alternative approach of reducing [ A | y ] to [ L | z ] instead. (a) Derive a method to solve [ L | z ]. You should give a general expression for finding x j for j = 1 ,...,n . (b) Describe a procedure for reducing [ A | y ] to [ L | z ]. 1
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Question 4 Professor W. Leontief (Nobel(Econ), 1973) was credited for his development of input-output analysis on independent industries. A basic fact used in his
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Unformatted text preview: analysis states that the total output is equal to the sum of external demand and internal consumption. Consider two companies A and B such that • for each $1 worth of the product company A produces, it requires $ a 11 of its own product and $ a 21 worth of the product B produces • for each $1 worth of the product company B produces, it requires $ a 12 of the product A produces and $ a 22 worth of its own product (a) Suppose that there is an external demand for $ d 1 of A’s goods and $ d 2 of B’s goods. Derive the necessary linear equations for Fnding the dollar values that A and B should produce. (b) Obtain the conditions for solving (a) for the three cases: a unique solution, no solution, and inFnity of solutions. ( Hint: Farlow (2007), p. 152 ) 2...
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  • Spring '10
  • Chan
  • Summation, Equals sign, gauss elimination, Chinese University of Hong Kong Department of Systems Engineering & Engineering Management

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