Math 237 1. Let f (x, y ) = 4 + x2 y 2.
Assignment 1 Solutions
i) Sketch the domain of f and state the range of f . Solution: The domain of f is 4 + x2 y 2 0 x2 y 2 4. The range is z 0.
ii) Sketch level curves and cross sections. Solution: Level Curves: k
AFM101MidtermExamAid
Chapter 1: Financial Statements and Business Decisions
Four Major Financial Statements (FS)
1) The Balance Sheet The companys financial position at a point in time ABC Co. Balance Sheet December 31, 2009 $XX XX $XX XX XX
Assets (list
Calculus 3
Course Notes for MATH 237 Edition 4.1
J. Wainwright and D. Wolczuk Department of Applied Mathematics
Copyright: J. Wainwright, August 1991 2nd Edition, July 1995 D. Wolczuk, 3rd Edition, April 2008 D. Wolczuk, 4th Edition, September 2009
Conten
Assignment 2
ACTSC231 (Mathematics of Finance), FALL 2010 Due: October 22(Friday) Hand in to the instructor in class To earn the credit of the assignment, you need to justify your answer. Simply listing the nal answer is unacceptable. I might only select
Math 235
Assignment 3
Due: Wednesday, May 26th
1. For each of the following pairs of vector spaces, dene an explicit isomorphism to establish that the spaces are isomorphic. Prove that your map is an isomorphism. a) P3 and R4 . b) The vector space P = cfw
Stat 230 - Assignment 2
Due in class on Wednesday, July 7, 2010
1. During a meteor shower, if you trace the trails of meteors back to their source, they appear to originate from a single point, called the radiant. This can be exhibited visually with a pho
Math 235
Assignment 2 Solutions
1. For each of the following linear transformations, determine a geometrically natural basis B and determine the matrix of the transformation with respect to B . a) perp(2,1,2) Solution: Pick v1 = (2, 1, 2). We want to pick
STAT 230
Solutions to Problems: Chapter 4
P ( B ) = 1 - P ( B ) = 0.6 P( A B) = 0 (mutually exclusive) P( A B) = 1 - P( A B) = 1
4.1 P ( A) = 1 - P ( A) = 0.75 P( A B) = P( A) + P( B) = 0.65
P ( A B ) = 1 - P ( A B ) = 0.35
A B = ( A B ) = = U so P ( A B
STAT 230
Solutions to Problems: Chapter 2
Note: Questions who solutions are not here are answered sufficiently well in the text. 2.4 a) Represent the letters by small letters, the envelopes by capitals. Note that pairs that are repeated from the previous
Math 235
Assignment 3 Solutions
1. For each of the following pairs of vector spaces, dene an explicit isomorphism to establish that the spaces are isomorphic. Prove that your map is an isomorphism. a) P3 and R4 . Solution: We dene L : P3 R4 by L(a3 x3 + a
STAT 230
Solutions to Problems: Chapter 3
Note: Questions who solutions are not here are answered sufficiently well in the text. 3.1 a) Notice that you can select the six digits in 7(6) ways. Now such a number is even if it ends with 2, 4, 6, or 8. Let's
Math 235
Assignment 4
Due: Wednesday, Jun 2nd
1. Prove that the product of two orthogonal matrices is an orthogonal matrix. 2. Prove that if R is an orthogonal matrix, then det R = 1. Give an example of a matrix A that has det A = 1, but is not orthogonal
STAT 230
Solutions to Problems: Chapter 4
P ( B ) = 1 - P ( B ) = 0.6 P( A B) = 0 (mutually exclusive) P( A B) = 1 - P( A B) = 1
4.1 P ( A) = 1 - P ( A) = 0.75 P( A B) = P( A) + P( B) = 0.65
P ( A B ) = 1 - P ( A B ) = 0.35
A B = ( A B ) = = U so P ( A B
Math 235
Assignment 4 Solutions
1. Prove that the product of two orthogonal matrices is an orthogonal matrix. Solution: Let P and Q be orthogonal matrices. Then we have (P Q)T (P Q) = QT P T P Q = QT Q = I, since P T P = I and QT Q = I . Thus P Q is also
Chapter 5 5.1 Lets use Fnn and Mnn to represent the events A female lives to age nn. and similar for a Male. a) If a female lives to 50, what is the probability she lives to 80 can be written P( F 50 F 80) P(F80|F50) = . Now notice that the set A80 = cfw_
STAT 230
Solutions to Problems: Chapter 3
Note: Questions who solutions are not here are answered sufficiently well in the text. 3.1 a) Notice that you can select the six digits in 7(6) ways. Now such a number is even if it ends with 2, 4, 6, or 8. Let's
Math 235
Assignment 1 Solutions
1. Let A be an m n matrix and B be an n p matrix. a) Prove that rank(AB ) rank(A). Solution: Since the rank of a matrix is equal to the dimension of its column space, we consider the column space of A and AB . Observe that
Problem Set 4: ACTSC 231 Mathematics of Finance, Fall 2010 Q1. (a) Noticing formulae sn i+ 1 sn = i+
i i
(1 + i)n 1 1 vn = and an i = , we immediately have i i 1
(1+i)n 1 i(1+i)n
i [(1 + i)n 1] + i i(1 + i)n i = = = (1 + i)n 1 (1 + i)n 1 (1 + i)n 1 = 1 .
AFM 101 Midterm Review
Brought edit Master subtitle 101 Click to to you by YOUR AFMstyle TAs
Things you SHOULD know
Financial Statements
Income statement Statement of Retained Earnings Balance Sheet Statement of Cash Flows
Journal Entries Deferral Vs.
Problem Set 5-solution: ACTSC 231 Mathematics of Finance, Fall 2010 Q1. The present value of this perpetuity-due is 1, 000v n = 6, 561; a where v = 9/10 i.e. d = 1/10. We know that = 1/d = 10. Thus, a n= ln(6, 561/10, 000) = 4. ln 0.9
Q2. We rst need to n
University of Waterloo Final Examination
Term: Fall Student Name UW Student ID Number Year: 2005
Course Abbreviation and Number Course Title Section(s) Instructor
AFM 101 Core Concepts of Accounting Information 001, 002, 003, 004 Duane Kennedy
Date of Exa
Math 235 1. Short Answer Problems
Term Test 1 Solutions
[2] a) By considering the dimension of the range or null space, determine the rank and p(0) the nullity of the linear mapping T : P2 R2 , where T (p(x) = . p(1) Solution: Range(T ) = R2 since T (1 x)
University of Waterloo Final Examination
Term: Fall Student Name Year: 2005
Solution
UW Student ID Number
Course Abbreviation and Number Course Title Section(s) Instructor
AFM 101 Core Concepts of Accounting Information 001, 002, 003, 004 Duane Kennedy
Da
Math 235 1. Short Answer Problems
Term Test 2 Solutions
[2] a) Let B = cfw_v1 , . . . , vk be an orthonormal basis for a subspace S of an inner product space V . Dene projS and perpS . Solution: Let v V , then projS (v ) and perpS (v ) are the unique vec
UNIVERSITY OF WATERLOO School of Accountancy
AFM 101 Professor Duane Kennedy Mid-Term Examination Fall 2005 Date and Time: October 28, 2005, 4:45 6:15pm Pages: 17, including cover Name: _ Student Number: _
Tutorial Number and Time: _ Instructions: 1) 2) C
Math 235
Assignment 0
Due: Not To Be Submitted
1. Determine projv x and perpv x where a) v = (2, 3, 2) and x = (4, 1, 3). b) v = (1, 2, 1, 3) and x = (2, 1, 2, 1). 2. Prove algebraically that projv (x) and perpv x are orthogonal. 3. Solve the system z1 (1
UNIVERSITY OF WATERLOO School of Accountancy
AFM 101 Professor Duane Kennedy Mid-Term Examination Fall 2005 Date and Time: October 28, 2005, 4:45 6:15pm Pages: 17, including cover Name: _
Solution_
Student Number: _
Tutorial Number and Time: _ Instruction
Math 235
Assignment 1
Due: Wednesday, May 12th
1. Let A be an m n matrix and B be an n p matrix. a) Prove that rank(AB ) rank(A). b) Prove that rank(AB ) rank(B ). c) Prove that if B is invertible, then rank(AB ) = rank(A). 2. Let T : V W be a linear mapp