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 lev
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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
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, Ap
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 listi
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
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
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) per
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 )
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 capital
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)
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
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
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 )
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
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
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
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, w
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(
AFM 101 Midterm Review
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Financial Statements
Income statement Statement of Retained Earnings Balance Sheet
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
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 I
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
University of Waterloo Final Examination
Term: Fall Student Name Year: 2005
Solution
UW Student ID Number
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AFM 101 Core Concepts of Acc
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
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 Numb
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
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_
St
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, th