Mathematical Economics - Exam 1 (Spring 2014) Answer Key
Instructions: In all proofs and analytical problems, be thorough, be careful and be sure to explain each
step. Often, when an error is made, partial credit depends on whether I can follow the reason
Problem set 2 answer key:
1. Exercise 2 By bringing the system into row echelon form, we obtain:
1
1
1
. When k 6= 1, rankA = 2 = number of equa0
1 k 0
tions=number of unknowns, so by Fact 7.11 (c.iii), the system has one
exactly solution. When k = 1, the
Problem set 1 answer key:
1. A.1.3 (a) We will show that (A\B)C AC [B C and AC [B C (A\B)C .
Let show rst that (A\B)C AC [B C . For this, take any x 2 (A\B)C
s
and we will show that x 2 AC [ B C . Since x 2 (A \ B)C , it follows that
x 2 A \ B. So either
Problem set 3 answer key:
1. 8.25 (b) Let A1 ; A2 ; :; An be square invertible matrices. Then
(A1 A2 : An )
1
= An 1 An 1 1 : A2 1 A1 1
(c) Let A
(1), B
( 1). Then, both A and B are invertible, but
A + B = (0), which is not invertible.
0 1
1
0 : 0
d1
1
B
Assignment 4 answer key:
a
b
a b
= ad bc;
c + ra d + rb
c d
ad + arb bc bra = ad bc
1. 9.6.
= a(d + rb)
b(c + ra) =
2. 26.16 (a) Let prove this by induction on the size of the determinant.
s
ra11
ra21
:
ran1
We want to show that P (n):
ra12
ra22
:
ran2
:
Mathematical Economics - Exam 1 (Spring 2015) answer key
Instructions: In all proofs and analytical problems, be thorough, be careful and be sure to explain each
step. Often, when an error is made, partial credit depends on whether I can follow the reason
Assignment # 1.
Due Tuesday, January 20th by 5PM in the main o ce at the Economics
Department (or in class or by email to [email protected]).
1. Exercise A1.3 (a,c)
2. Exercise 7.2 (a) (solve the system by substitution and by elimination of
variable
Assignment # 2.
Due Tuesday, January 27th in class or by email to the TA, Lijuan Feng at
[email protected]
1. Exercise 7.21 (iii, iv, v)
2. Use the rank criterion (Fact 7.11 on page 147) to determine for what values
of the parameter k the system:
x
Mathematical Economics - Exam 2 (Spring 2014)
Instructions: In all proofs and analytical problems, be thorough, be careful and be sure to explain each
step. Often, when an error is made, partial credit depends on whether I can follow the reasoning. The
to
Mathematical Economics - Exam 3 (Fall 2014)
Instructions: In all proofs and analytical problems, be thorough, be careful and be sure to
explain each step. Often, when an error is made, partial credit depends on whether I can follow
the reasoning. The tota
Mathematical Economics - Exam 1 (Spring 2014)
Instructions: In all proofs and analytical problems, be thorough, be careful and be sure to explain each
step. Often, when an error is made, partial credit depends on whether I can follow the reasoning. The
to
Mathematical Economics - Exam 1 (Fall 2014)
Instructions: In all proofs and analytical problems, be thorough, be careful and be sure to explain each
step. Often, when an error is made, partial credit depends on whether I can follow the reasoning. The
tota
Mathematical Economics - Exam 2 (Fall 2014)
Instructions: In all proofs and analytical problems, be thorough, be careful and be sure to explain each
step. Often, when an error is made, partial credit depends on whether I can follow the reasoning. The
tota
Mathematical Economics - Exam 1 (Fall 2014)
Instructions: In all proofs and analytical problems, be thorough, be careful and be sure to explain each
step. Often, when an error is made, partial credit depends on whether I can follow the reasoning. The
tota
Mathematical Economics - Exam 2 (Fall 2014) Answer Key
Instructions: In all proofs and analytical problems, be thorough, be careful and be sure to explain each
step. Often, when an error is made, partial credit depends on whether I can follow the reasonin
Mathematical Economics - Exam 2 (Spring 2014) - answer key
Instructions: In all proofs and analytical problems, be thorough, be careful and be sure to explain each
step. Often, when an error is made, partial credit depends on whether I can follow the reas
Mathematical Economics - Exam 3 (Fall 2014) - answer key
Instructions: In all proofs and analytical problems, be thorough, be careful and be sure to
explain each step. Often, when an error is made, partial credit depends on whether I can follow
the reason
Mathematical Economics - Exam 3 (Spring 2014) answer key
Instructions: In all proofs and analytical problems, be thorough, be careful and be sure to
explain each step. Often, when an error is made, partial credit depends on whether I can follow
the reason
Mathematical Economics - Exam 3 (Spring 2014)
Instructions: In all proofs and analytical problems, be thorough, be careful and be sure to
explain each step. Often, when an error is made, partial credit depends on whether I can follow
the reasoning. The to
Assignment # 3.
Due Tuesday, February 3rd by 5PM in the main o ce at the Economics
Department (or in class or by email to [email protected]).
1. Exercise 8.25 (b,c)
2. Exercise 8.28
3. Exercise 8.29
4. Exercise A.1.4. (for this exercise, follow the