01samp1

01samp1 - Mathematical Economics Midterm #1, October 2,...

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Mathematical Economics Midterm #1, October 2, 2000 You have until 4:45 to complete this exam. Answer all fve questions. Each question is worth 20 points, For a total oF 100 points. Good luck! 1. (Linear Systems) Consider the linear system x + y + z = 13 x + 5 y + 10 z = 61 . Show that this system has solutions. How many solutions are there? Can you fnd a solution where x , y , and z are all positive integers? 2. (Matrices) Let A and B be n × n matrices. Show that iF ( A + B ) 2 = A 2 + 2 AB + B 2 , then AB = BA . 3. (Determinant) Consider the matrix A = ± 3 - 4 - 1 0 ² ±ind all λ so that det( A - λI ) = 0. 4. (Linear Systems) Demand For good 1 is e 1 - ap 1 + bp 2 ; demand For good 2 is e 2 + cp 1 - dp 2 ; the supply oF good i is s i . Here a , b , c , d , e i , and s i
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This note was uploaded on 01/01/2012 for the course ECO 7405 taught by Professor Staff during the Fall '08 term at FIU.

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