Temple University

	Department of Economics

	Economics 615

	Linear Algebra

1.  Given the transformation equations

	

a.  Evaluate the Jacobian

	

b.  Also evaluate

	

by solving the transformation equations for Y₁ and Y₂.
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 a₀, a₁ and b₀, b₁ to denote the roots of A and B, respectively. Calculate a₀ x a₁ x b₀ x b₁.
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?