EXCURSIONS IN MODERN MATH
5th Edition
ISBN: 9781323741559
Author: Tannenbaum
Publisher: PEARSON C
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Textbook Question
Chapter 3, Problem 52E
Three players
Figure
a. Which items go to A?
b. Which items go to B?
c. Which items go to C?
d. Which items are left over?
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16. Solve the given differential equation:
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Given,
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R denotes the field of real numbers, Q denotes the field of rationals, and
Fp denotes the field of p elements given by integers modulo p. You may refer to general
results from lectures.
Question 1
For each non-negative integer m, let R[x]m denote the
vector space consisting of the polynomials in x with coefficients in R and of degree ≤ m.
x²+2, V3 = 5. Prove that (V1, V2, V3) is a linearly independent
(a) Let vi = x, V2 =
list in R[x] 3.
(b) Let V1, V2, V3 be as defined in (a). Find a vector v € R[×]3 such that (V1, V2, V3, V4)
is a basis of R[x] 3.
[8]
[6]
(c) Prove that the map ƒ from R[x] 2 to R[x]3 given by f(p(x)) = xp(x) — xp(0) is a
linear map.
[6]
(d) Write down the matrix for the map ƒ defined in (c) with respect to the basis
(2,2x + 1, x²) of R[x] 2 and the basis (1, x, x², x³) of R[x] 3.
[5]
Question 4
(a) The following matrices represent linear maps on R² with respect to an
orthonormal basis:
=
[1/√5 2/√5
[2/√5 -1/√5]
"
[1/√5 2/√5]
A =
B =
[2/√5 1/√5] 1
C =
D =
=
=
[ 1/3/5 2/35]
1/√5 2/√5
-2/√5 1/√5'
For each of the matrices A, B, C, D, state whether it represents a self-adjoint
linear map, an orthogonal linear map, both, or neither.
(b) For the quadratic form
q(x, y, z) = y² + 2xy +2yz
over R, write down a linear change of variables to u, v, w such that q in these
terms is in canonical form for Sylvester's Law of Inertia.
[6]
[4]
Chapter 3 Solutions
EXCURSIONS IN MODERN MATH
Ch. 3 - Henry, Tom, and Fred are breaking up their...Ch. 3 - Alice, Bob, and Carlos are dividing among...Ch. 3 - Angie, Bev, Ceci, and Dina are dividing among...Ch. 3 - Mark, Tim, Maia, and Kelly are dividing among...Ch. 3 - Allen, Brady, Cody, and Diane are sharing a cake....Ch. 3 - Carlos, Sonya, Tanner, and Wen are sharing a cake....Ch. 3 - Four partners Adams, Benson, Cagle, and Duncan...Ch. 3 - Prob. 8ECh. 3 - Suppose that Angelina values strawberry cake twice...Ch. 3 - Suppose that Brad values chocolate cake thrice as...
Ch. 3 - Suppose that Brad values chocolate cake four as...Ch. 3 - Suppose that Angelina values strawberry cake five...Ch. 3 - Karla and five other friends jointly buy the...Ch. 3 - Marla and five other friends jointly buy the...Ch. 3 - Suppose that they flip a coin and Jackie ends up...Ch. 3 - Suppose they flip a coin and Karla ends up being...Ch. 3 - Suppose that they flip a coin and Martha ends up...Ch. 3 - Suppose that they flip a coin and Nick ends up...Ch. 3 - Suppose that David is the divider and Paula is the...Ch. 3 - Suppose that Paula is the divider and David is the...Ch. 3 - Three partners are dividing a plot of land among...Ch. 3 - Three partners are dividing a plot of land among...Ch. 3 - Four partners are dividing a plot of land among...Ch. 3 - Four partners are dividing a plot of land among...Ch. 3 - Mark, Tim, Maia, and Kelly are dividing a cake...Ch. 3 - Allen, Brady, Cody; and Diane are sharing a cake...Ch. 3 - Prob. 27ECh. 3 - Four partners are dividing a plot of land among...Ch. 3 - Prob. 29ECh. 3 - Five players are dividing a cake among themselves...Ch. 3 - Four partners Egan, Fine, Gong, and Hart jointly...Ch. 3 - Four players Abe, Betty, Cory, and Dana are...Ch. 3 - Exercises 33 and 34 refer to the following...Ch. 3 - Exercises 33 and 34 refer to the following...Ch. 3 - Exercise 35 through 38 refer to the following...Ch. 3 - Exercise 35 through 38 refer to the following...Ch. 3 - Prob. 37ECh. 3 - Prob. 38ECh. 3 - Exercises 39 and 40 refer to the following:...Ch. 3 - Exercises 39 and 40 refer to the following:...Ch. 3 - Jackie, Karla, and Lori are dividing the foot-long...Ch. 3 - Jackie, Karla, and Lori are dividing the foot-long...Ch. 3 - Ana, Belle, and Chloe are dividing four pieces of...Ch. 3 - Andre, Bea, and Chad are dividing an estate...Ch. 3 - Five heirs A,B,C,D, and E are dividing an estate...Ch. 3 - Oscar, Bert, and Ernie are using the method of...Ch. 3 - Anne, Bette, and Chia jointly own a flower shop....Ch. 3 - Al, Ben and Cal jointly own a fruit stand. They...Ch. 3 - Ali, Briana, and Caren are roommates planning to...Ch. 3 - Anne, Bess and Cindy are the roommates planning to...Ch. 3 - Prob. 51ECh. 3 - Three players (A,B and C) are dividing the array...Ch. 3 - Three players (A,B,andC) are dividing the array of...Ch. 3 - Three players (A,B,andC) are dividing the array of...Ch. 3 - Five players (A,B,C,D,andE) are dividing the array...Ch. 3 - Four players (A,B,C,andD) are dividing the array...Ch. 3 - Prob. 57ECh. 3 - Queenie, Roxy, and Sophie are dividing a set of 15...Ch. 3 - Ana, Belle, and Chloe are dividing 3 Choko bars, 3...Ch. 3 - Prob. 60ECh. 3 - Prob. 61ECh. 3 - Prob. 62ECh. 3 - Prob. 63ECh. 3 - Prob. 64ECh. 3 - Three players A, B, and C are sharing the...Ch. 3 - Angeline and Brad are planning to divide the...Ch. 3 - Prob. 67ECh. 3 - Efficient and envy-free fair divisions. A fair...Ch. 3 - Suppose that N players bid on M items using the...Ch. 3 - Asymmetric method of sealed bids. Suppose that an...Ch. 3 - Prob. 73E
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