Temple University Department of EconomicsEconomics 615 Linear Algebra1. Given the transformation equations

a. Evaluate the Jacobian

b. Also evaluate

by solving the transformation equations for Y_{1} and Y_{2}.

c. Show that the absolute value of K^{*} is equal to the inverse of the absolute
value of J.

2. a. Find the characteristic roots of each of the following matrices:

b. Use a_{0}, a_{1} and b_{0}, b_{1} to denote the roots
of A and B, respectively. Calculate a_{0} x a_{1} x b_{0} x b_{1}.

c. Now find the characteristic roots of A'B, AB' and AB. There are two roots for each
matrix.

d. For each of the matrices in part c, multiply the pair of roots. What is the
relationship between these products and that in part b?