Determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text.
(a) The matrix of cofactors of a square matrix A is the adjoint of A.
(b) In Cramer’s Rule, the denominator is the determinant of the matrix formed by replacing the column corresponding to the variable being solved for with the column representing the constants.

Determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text.
(a) The column space of a matrix A is equal to the row space of A^T.
(b) The row space of a matrix A is equal to the column space of A^T.

Determine whether each statement is true or false 
(a) The set of the five worst U.S. presidents is well-defined.
(b) 10 ∈ {1, 2, 3, · · · , 16, 17, 18}
(c) 6 ∈ {x | x ∈ N and x is an even number}
(d) Set {φ, 0} is an empty set.
(e) Empty set is a subset of all sets.
(f) {Ralph, Alice} ⊆ {Alice, Trixie, Norton, Ralph}
(g) The set of all fractions between 0 and 1 is finite.
(h) If A = {1, 2, 3, 4, 5} and B = {one, two, three, four, five} then A = B.
(i) {e} ∈ {a, e, i, o, u}
(j) Mickey Mouse ∈ {characters created by Walt Disney}

Determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text.
(a) To find the determinant of a triangular matrix, add the entries on the main diagonal.
(b) To find the determinant of a matrix, expand by cofactors in any row or column.
(c) When expanding by cofactors, you need not evaluate the cofactors of zero entries.

Determine whether each statement is true, false, or uncertain and explain why.
i. The resources at the disposal of Mrs. Do Good can allow her produce at the points on her productions possibilities frontier. It can therefore be said that points inside the PPF are attainable and efficient and while points outside her PPF are inefficient and unattainable.
ii. “An inferior good will always be inferior throughout the full range of incomes experienced by consumers.”
iii. The “wants” of an individual can be equated to his/her “needs” in absolute sense.
2.
Consider the following model for the toothbrush market in Girne. Suppose the aggregate demand for brushes in Girne is given by ( ⁄ ) where P denotes the price and Q denotes the quantity of brushes in terms of thousands of brushes demanded. The aggregate Supply for brushes in Girne is given by
.
a. Compute the toothbrush market equilibrium. What are the equilibrium price and quantity?
b. Now suppose a tax of t = 60TL is imposed on each brush that is produced. Compute the brush market
equilibrium with the tax. What are the equilibrium price and quantity?
c. What price will the consumers of toothbrush pay and what amount will producers receive?
d. Graph (a) to (b)
e. Who bears the brunt of the tax and by how much?
f. What is the tax revenue to the government?
3.
i) Calculate the cross-price elasticities in case of a decrease in the price of cabbages with 20 percent, an increase in the demand for tomatoes with 15 percent and a decrease in the demand for asparagus with 10 percent. Comment on whether tomatoes and asparagus can substitute or complement the cabbage. Use appropriate equations where possible.
ii) Three months after graduating from GAU you get a promotion and a 20% raise. Your consumption habits change accordingly. Use the following information to determine your income elasticity of demand and state whether the good is a normal good or inferior good.
a. You consume 10% fewer frozen hot dogs.
b. You consume 5% more pork chops.