Solutions to Homework 12.
Math 110, Fall 2006. Prob 6.1.1. (a) True, directly by definition. (b) True, this is also required by the definition. (c) False, it is linear in the first component and conjugate linear in the second component. (d) False, there a
Computation of the Poisson Distribution
n
y
P(Y = y) = lim
n
n!
= lim
n y!(n y)! n
y
n
y
1
1
ny
n
ny
n
y
n (n 1) (n y + 1)
= lim
1
n y! n
n
n
n
y
n (n 1) (n y + 1)
= lim
1
n y! n
n
n
n
1
=
y
y!
= e
lim
n
y
y!
1
n
n
y
n
n
1
y1
1
1
n
n
= lim
1
n y!
Course description and aims
In this course, students will be introduced to more topics of
mathematics commonly applied in engineering so that students could
be further enhanced with a concrete skill in mathematics underpinned
for different engineering sub
[Last Name] 1
[Your Name]
[Instructor Name]
[Course Number]
[Date]
[Title]: [Subtitle]
[Research papers that use MLA format do not include a cover page unless requested by
your instructor. Instead, start with the information shown. Do not bold the title o
1.
(a) What regular polyhedron can be made from the above net?
(b) How many vertices does it have?
(c) Which point(s) is/are joined to point D?
2.
Draw the front view, side view and top view of the
solid below.
3.
The figure shows the front view, side vie
201415 Second Semester
MATH 2911/3911 Game Theory and Strategy
Chapter 2: Two-Person Zero-Sum Games
A.
Representing Games
(Ref: Sections 2.12.2)
1.
A game (particularly a sequential game) can be represented in extensive form by drawing a
tree graph (also
Solutions to Homework 1.
Math 110, Fall 2006. Prob 1.2.1. (a) True this is axiom (VS 3). (b) False we proved the zero vector is unique. (c) False: take x to be the zero vector, and take any scalars a and b. (d) False: take a to be the zero scalar and any
Solutions to Homework 2.
Math 110, Fall 2006. Prob 1.4.4. (a) Yes, since the linear system a+b 2a + 3b -a a-b has a solution a = 3, b = -2. (b) No, the corresponding linear system has no solution. (c) Yes, the corresponding linear system has a solution a
Solutions to Homework 3.
Math 110, Fall 2006. Prob 2.1.10. By the linearity of T , we use the fact (1, 0) + 3(1, 1) = (2, 3) to obtain T (2, 3) = T (1, 0) + 3T (1, 1) = (1, 4) + 3(2, 5) = (5, 11). The map T is 1 1 as we see that T (a(1, 0) + b(1, 1) = a(1
Solutions to Homework 4.
Math 110, Fall 2006. Prob 2.3.13. Let A = [aij ]. Then At = [aji ], and
n n
tr(A) =
i=1
aii =
j=1
ajj = tr(At ).
The elements of A = [aij ], B = [bij ], AB = [cij ] and BA = [dij ] are connected by the formulas
n n
cij =
k=1
aik b
Solutions to Homework 6.
Math 110, Fall 2006. Prob 2.7.1. (a) True. (b) True. (c) False: the roots of the auxiliary polynomial give frequencies of solutions. (d) False: linear combinations of these are solutions too. (e) True: directly from linearity and
Solutions to Homework 8.
Math 110, Fall 2006. Prob 4.1.1. (a) False, it is 2-linear. (b) True. (c) False, A is invertible if and only if det(A) = 0. (d) False, it is the absolute value of that determinant. (e) True (proved in this section). Prob 4.1.2. (a
Solutions to Homework 9.
Math 110, Fall 2006. Prob 4.3.10. Since det(AB) = det(A) det(B) for any two square matrices of the same order, this implies, by induction, that (det M )k = det(M k ) for all k IN. Since the determinant of the zero matrix is zero,
Solutions to Homework 10.
Math 110, Fall 2006. Prob 5.1.3. (a) The eigenvalues are 1 and 4, with the eigenspaces E1 = spancfw_[1 1]t , E4 = t spancfw_[2 3] . The vectors [1 1]t , [2 3]t form a basis for IR2 . The matrix Q diagonalizes A, where Q= 1 1 2 3
Solutions to Homework 11.
Math 110, Fall 2006. Prob 5.4.1. (a) False, cfw_0 and the whole space are T -invariant for any T . (b) True (Theorem 5.21). (c) False: just take w to be a nonzero multiple of v, then the corresponding T -cyclic subspaces are the
201415 Second Semester
MATH 2911/3911 Game Theory and Strategy
Chapter 8: Evolutionary Games
A.
Introduction
(Ref: Section 8.1)
1.
(a) What do you know about evolution?
(b) In our previous study of game theory, most of them we expect an individual to make
MATH1851 - Calculus and Ordinary Differential Equations
Second Semester 2014-15
Course description
Part 1.
Differential and Integral Calculus (Single Variable): Limits and continuity; Rates of
change; Derivatives of trigonometric functions, inverse trigon