ums08mt02ans

ums08mt02ans - New York University Department of Economics...

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New York University Department of Economics V31.0006 C. Wilson Mathematics for Economists April 2, 2009 Spring 2008 Midterm II Answer Key The value of each question is given in the parenthesis. 1. (5) Write your name and a 4 digit ID (the same one used on the f rst midterm) on the cover of two exam booklets. Label one of the booklets 2-4 ,another 5-7. Answer each question below in its corresponding booklet. Begin each question on a separate page. 2. (12) Let x =(3 , 4) and y =(2 , 1) . (a) Plot each of the following in the same graph i. x ii. y iii. x 2 y (b) Compute the following i. h x, y i h x, y i =3 · 2+4 · 1=10 . ii. k x k k x k = 3 2 +4 2 = 25 = 5 (c) Express the vector z =(5 , 5) as a linear combination of x and y and illustrate graphically. z = λx + μy implies 5=3 λ +2 μ 5=4 λ + μ Solving for λ and μ ,weobta in λ = μ =1 . So z = x + y. http://homepages.nyu.edu/ caw1/
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V31.0006: Spring 2008 Midterm II Answer Key April 2, 2009 Page 2 3. (16) De f ne the following. (a) Linear Space. V is a linear space if for all x, y V and λ R ,wehave x + y V λx V. (b) A nonsingular matrix. An n × n matrix A is nonsingular if Ax =0 implies x . (c) Convex set. X R n is convex if for all x, y X and λ [0 , 1] , we have λx +(1 λ ) y X. (d) Positive de f nite matrix. A symmetric matrix is positive de f nite if x · Ax > 0 for all x 6 .
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This note was uploaded on 12/14/2009 for the course BICD BICD 110 taught by Professor Zao during the Winter '09 term at UCSD.

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ums08mt02ans - New York University Department of Economics...

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