Math for Econ II Homework 6 - Math for Econ II Written Assignment 6(28 points Due Friday October 24 Jankowski Fall 2014 Please write neat solutions for

Math for Econ II Homework 6 - Math for Econ II Written...

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Math for Econ II, Written Assignment 6 (28 points) Due Friday, October 24 Jankowski, Fall 2014 Please write neat solutions for the problems below. Show all your work. If you only write the answer with no work, you will not be given any credit. Write your name and recitation section number. Staple your homework if you have multiple pages! 1. (3 pts) Find all numbersxsuch thatx0-112x-13-201= 5.2. (4 pts) Find123410-124200400-3-6-9-12400111.3. (4 pts) There are 2×2 matricesAsuch thatA2=-I2. For example, ifA=0-110, thenA2=-I2.Is there a 3×3 matrixAsuch thatA2=-I3? If so, find such anA. If not, show no suchAexists.(hint: use the fact that ifXandYaren×nmatrices then|XY|=|X||Y|)4. Solve the following systems by finding the inverse of the coefficient matrix.(a) (2 pts)2x-7y=83x-4y=11(b) (4 pts)2x+ 4y-z=15x-3y+ 2z=-56x+ 5y+z=285. An economy has three markets with supply and demand functions for the three goods given byqS1=-20 + 3p1-p2qD1= 255-2p1-p3qS2=-125 + 2p2-p1-p3qD2= 200-p2qS3= 4p3-2p1qD3= 225-2p3-p1(a) (3 pts) Find a matrix equation of the formAp1p2p3=bthat will allow us to solve for the equilibrium prices.In (b) and (c), find the equilibrium prices in two different ways:(b) (4 pts) By findingA-1and using it to solve the system.(c) (4 pts) By using Cramer’s rule.

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