Name of university
Marketing in Travel and Tourism
Student name
Date
Name of professor
Course number
Surname 2
Introduction
Marketing plays a role of creating serene environment for the sellers and buyers. Organizations
and various other businesses must a
Quiz 1, Math 571, 6 September, 2016
Name:
Solutions
1. (10 points): Let A Cmn , with m n. Prove that AH A is invertible if and only
if A has full rank.
Proof: () Suppose that A has full rank and x N(AH A) Cn , i.e, AH Ax = 0.
Then xH AH Ax = 0. In other w
Quiz VI, Math 571, 22 November, 2011
Name:
Solutions
1. (30 points): Let A = diag(a, b) R22 , a > b > 0, b = 0, and x = 0. Demonstrate the zigzag phenomenon for the steepest descent method, by showing that if
xi = ci (b, sa)T , for some ci R , where s = 1
Quiz V, Math 571, 3 November, 2011
Name:
Solutions
1. (15 points): Let A Cnn . Prove that A is convergent if and only if limk Ak x =
0 for any vector x Cn .
Proof: () Suppose that A is convergent. Let x Cn be arbitrary. Then for any
> 0 there is a positiv
Quiz IV, Math 571, 27 October, 2011
Name:
1. (15 points): Let A Cmn , m n, and b Cm . Prove that the vector x Cn is
a least squares solution to Ax = b if and only if r R(A) , where r := b Ax.
Proof: () Dene
q (w) := b Aw
2
2
,
for all w Cn . Suppose that
Quiz III, Math 571, 6 October, 2011
Name:
Solutions
1. points): Suppose A Cnn is HPD. Dene x A : Cn R via x
(15
xH Ax. Show that this norm satises the triangle inequality.
:=
A
Proof: Let us prove x + y 2 ( x A + y A )2 , for if this is true, using the fa
Quiz II, Math 571, 27 September, 2011
Name:
Solutions
1. (15 points): Suppose that A Cnn and (A) (0, ). Prove that A is HPD.
her
Proof: Since A Cnn , there exists a unitary matrix U and a diagonal matrix
her
D = diag (1 , . . . , n ), where i (A), for i =
Quiz I, Math 571, 8 September, 2011
Name:
Solutions
1. (15 points): Consider the induced matrix 2-norm
A
where
2
= sup
2
xCm
2
: Cmm R, dened via
Ax 2
,
x2
is the vector two norm and Cm := Cm \ cfw_0. Prove that
A
2
= max
1im
i ,
where the i are the eig
Midterm Exam, Math 571
13 October, 2011
Name:
Solutions
1. (10 points): Let A Cmn , m n, with rank(A) = n. Prove that the reduced
QR factorization A = QR with the normalization rjj > 0 is unique.
Proof: Since A has full rank, AH A Cnn is invertible and, i
Programming Exercise, Math 571
10 November, 2011
Name:
Due:
Final Exam
Use the nite dierence method to approximate the solution of the Poisson problem:
u := xx u yy u = f ,
u=0,
in
on
= (0, 1) (0, 1) ,
,
where f is a given function. Specically, solve th
Homework 13, Math 571
24 November, 2011
Name:
1. Suppose that the spectrum of A Rnn is denoted (A) = cfw_1 , . . . , n R and
sym
has the following ordering
|1 | > |2 | |n | 0.
Let S = cfw_x1 , . . . , xn be an orthonormal basis of eigenvectors of A, wit
Running head: PROJECT PLAN INCEPTION
Project Plan Inception
Student Name
Course
Date
1
PROJECT PLAN INCEPTION
2
Project Plan Inception
Introduction
CompTIA Inc. is a multimillion dollar company whose business is to collect and analyze
data. The company ha
3. a) Independent variable- Temperature
Dependent variable- Beer Sales
An increase in temperature has a subsequent direct increase on the number of beers sold.
R2=1-6d2/n3-n: R2=+1,
The data is highly, positively correlated on calculation by Spearman rank
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Homework 12, Math 571
17 November, 2011
Name:
1. Let the CG algorithm be applied to solve Ax = b where A Rnn is SPD and
b Rn . Prove that, if the iteration has not already converged (ri1 = 0), then
xi is the unique vector in Ki (b, A) that minimizes the f
Homework 11, Math 571
10 November, 2011
Name:
1. Let A = diag(a, b) R22 , a > b > 0, b = 0, and x = 0.
(a) Sketch some level curves of
1
f (z) = zT Az zT b .
2
(b) Find the condition number of A.
(c) Compute the theoretical convergence rate of the steepes
Homework 10, Math 571
3 November, 2011
Name:
1. A General Descent Method: Suppose that A Rnn is SPD, b Rn and
x = A1 b Rn . Dene the quadratic function f : Rn R via
1
f (z) = zT Az zT b .
2
Fix a search direction s Rn .
(a) Show that
:= arg min f (w + s)
Final Exam, Math 571
8 December, 2009
Name:
Solutions
1. (10 points): Let F Crr be a Householder reector. Determine the eigenvalues,
determinant, and singular values of F and give details of your calculations.
Solution: (eigenvalues:) F has the form F = I
Midterm Exam, Math 571
8 October, 2009
Name:
Solutions
1. (10 points): Let u, v Cm and dene A = I + uv . (a) Show that if A is
invertible, then the inverse has the form A1 = I + uv , for some scalar . Give
an expression in this case. (b) For what u and v
Homework 10, Math 571
12 November, 2009
Name:
1. Suppose that A Rnn is SPD and dene the quadratic function f : Rn R via
Dene rn1
1
f (x) = xT Ax xT b .
2
:= b Axn1 . Prove that
n := arg min f (xn1 + rn1 ) =
R
rT1 rn1
n
.
rT1 Arn1
n
2. Dene A Rmm via
0
.
.