Math 545
Homework # 5: due Mar 22, 2017
1. For an n n Fourier matrix F :
(a) calculate F F , and use this to find F 1 ;
(b) find a permutation of the columns of F that produces F , so that F P = F ;
(c) use these to find F 2 and F 4 .
2. Let w be a primit
Econ 104: Introduction to MacroeconomicsProf. LarudeeFall 2015
Problem set 4 (due Nov. 5-6)
1a. Suppose the required reserve ratio is 5%. Then when the Fed buys
$500 worth of bonds from someone, and that person deposits the
money in a checking account in
Luke Cabell
Debate Talking Points
Ms. Withrow
November 17, 2015
Increase Taxes and Decrease Government Spending
Increasing taxes on the rich and decreasing government spending.
1.Spending cuts do much less damage to growth than tax increases. (Furth)
In a
CHARACTER ANALYSIS
Acting Fundamentals Monologue and Scene Study
Luke Cabell
Title of Play: Stop Kiss
Act and Scene: Scene Eight
CHARACTER DESCRIPTION, LOCATION & RELATIONSHIPS
Character Name(s): George
Age: Late 20s to early 30s
Physical Description from
Title: Mohandas Gandhi.
By: Rushdie, Salman, Time, 0040781X, 4/13/1998, Vol. 151, Issue 14
BORN Oct. 2, 1869, in Porbandar, India
1893 Goes to South Africa and battles for the rights of Indians
1915-20 Begins his
The third edition of The Trial and Death of Socrates
presents G. M. A. Grube’s distinguished translations, as
revised by John Cooper for Plato, Complete Works
(Hackett, 1997). Cooper has also contributed a
number of new or expanded footnotes and Suggestio
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Citation: 25 Loy. U. Chi. L.J. 507 1993-1994
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You know why I had no address for three months? I stole a suit in Kansas City
and I was jailed. I stole myself out of every good job since high school. And I
never got anywhere because you blew me so full of hot air I could never stand
taking orders from
Jinguo Lian
Math437 Notes
September 8, 2015
1
The Measurement of Interest
1.1
1(a)-1(v)
Example 1. If you have borrowed $100 from Tom and you promised to pay back $105 after
one year then Tom is making a profit of $5, which is the fee for borrowing his mo
Math 545
Homework # 4: due Mar 1, 2017
1. Use Gram-Schmidt to compute the QR decomposition of the matrix
1 10 10
1
4 4
.
A=
1 4
6
1 2 8
2. Use Gram-Schmidt to generate an orthonormal basis from the independent set x2 , 1, x ,
using the inner product
Math 545
Homework # 3: due Feb 17, 2017
1. Assume that the vectors w1 , w2 and w3 are linearly independent.
(a) Show that the differences
v 1 = w2 w1 ,
v2 = w3 w2
and v3 = w1 w3
are dependent by exhibiting an appropriate linear combination.
(b) Show that
Math 545
Homework # 8: due Apr 21, 2017
1. Without multiplying
A=
cos sin
sin cos
0
0
cos sin
sin cos
,
find the eigenvalues and eigenvectors of A, and give conditions under which A is positive
definite.
2. Given the matrix
A=
2/5
1
11/5
2
!
,
diag
Math 425 Section 02
Homework 7
Due: Monday, April 24
See the homework instructions posted on Moodle.
Reference: Sections 7.1 through 7.6 of Vector Calculus by Marsden & Tromba.
1. [6 points] Let f (x, y, z) = y and c(t) = (0, 0, t) for 0 t 1. Show that
R
Math 545
Homework # 6: due Apr 3, 2017
1. (a) Argue that the characteristic polynomial of A can be written
pA () = det(A I) = (1 )(2 ) . . . (n ),
where j are the eigenvalues.
(b) Use (a) to show that the determinant is the product of the eigenvalues.
(c)
Math 545
Homework # 7: due Apr 12, 2017
1. (a) Which of the following classes of matrices does P belong to: orthogonal, invertible,
Hermitian, unitary, factorizable into LU , factorizable into QR?
0 1 0
P = 0 0 1 .
1 0 0
(b) Compute P 2 , P 3 and P 100 .
Math 545
Homework # 2: due Feb 10, 2017
1. For each map, decide whether it is linear or not. If not, explain why not, and if so, express
it as a matrix in the given basis.
(a) f : R3 R3 given by f (x, y, z) = (x 2y, x + y + xz, x 5z), using the standard
b
Math 425 Section 02
Homework 6
Due: Friday, April 14
See the homework instructions posted on Moodle.
Reference: Sections 6.1 through 6.3 of Vector Calculus by Marsden & Tromba.
[10 points per problem]
x y x + y
1. Let T (x , y ) =
,
. Let D = [0, 1] [
Math 545
Homework # 1: due Feb 1, 2017
1. Decide, with reasons, whether or not the following are vector spaces:
(a) Solutions of the algebraic equations
2 x + 3 y = z,
3 x 2 y + z = 1;
(b) cfw_u R3 | u1 0;
(c) Solutions of the differential equation
m
dx
d
1947: The End of the Raj
Edidin, Peter
New York Times Upfront; Jan 30, 2006; 138, 9; ProQuest Social Sciences Premium Collection
pg. 16
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