{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

01samp1 - Mathematical Economics Midterm#1 October 2 2000...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Mathematical Economics Midterm #1, October 2, 2000 You have until 4:45 to complete this exam. Answer all five 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 find 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 Find 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
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}