Questions which review material from Week 1:
1. If a mass m is placed at the end of a spring, and if the mass is pulled downwards and released,
the mass-spring system will begin to oscillate. The displacement y of the mass from its resting
position is giv
University of Newcastle
School of Mathematical and Physical Sciences
MATH2320 - Linear Algebra
Workshop 2 (Week 3)
The textbook is Linear Algebra Done Right by Sheldon Axler, 2nd ed or later. This
Workshop covers Lecture 3 (2.1 Span and Linear Independenc
University of Newcastle
School of Mathematical and Physical Sciences
MATH2320 - Linear Algebra
Workshop 7 (Week 8)
The textbook is Linear Algebra Done Right by Sheldon Axler, 2nd ed or later. This
Workshop covers the last part of Lecture 13 (8.6 Jordan Fo
University of Newcastle
School of Mathematical and Physical Sciences
MATH2320 - Linear Algebra
Workshop 3 (Week 4)
The textbook is Linear Algebra Done Right by Sheldon Axler, 2nd ed or later. This
Workshop covers Lecture 5 (3.1 Definitions and Examples, 3
University of Newcastle
School of Mathematical and Physical Sciences
MATH2320 - Linear Algebra
Workshop 5 (Week 6)
The textbook is Linear Algebra Done Right by Sheldon Axler, 2nd ed or later. This
Workshop covers Lecture 9 (5.3 Upper-Triangular Matrices,
University of Newcastle
School of Mathematical and Physical Sciences
MATH2320 - Linear Algebra
Workshop 8 (Week 9)
The textbook is Linear Algebra Done Right by Sheldon Axler, 2nd ed or later. This
Workshop covers Lecture 15 (6.2 Norms, 6.3 Orthonormal Bas
University of Newcastle
School of Mathematical and Physical Sciences
MATH2320 - Linear Algebra
Workshop 9 (Week 10)
The textbook is Linear Algebra Done Right by Sheldon Axler, 2nd ed or later. This
Workshop covers Lecture 16 (6.4 Orthogonal Projections an
Nombre de la materia
Estadstica y probabilidad
Nombre de la Licenciatura
Ing. Industrial y Administracin
Nombre del alumno
Oscar Daniel Espinoza cebreros
Matrcula
000031331
Nombre de la Tarea
Muestreo aleatorio
Unidad # 5
Nombre del Tutor
Veronica Rodrigu
d
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10-15% National Income and Price
Determination
A. Aggregate demand
1. Determinants of aggregate demand
2. Multiplier and crowding-out effects
B. Aggregate supply
1. Short-run and long-run analyses
2. Sticky versus flexible wages and prices
3. Determinants
15-20% Financial Sector
(Money and Banking)
A. Money, banking, and financial markets
1. Definition of financial assets: money, stocks, bonds
2. Time value of money (present and future value)
3. Measures of money supply
4. Banks and creation of money
5. Mo
University of Newcastle
School of Mathematical and Physical Sciences
MATH2320 - Linear Algebra
Workshop 1 (Week 2)
WELCOME TO YOUR FIRST MATH2320 WORKSHOP!
My Demonstrators name is:
The textbook is Linear Algebra Done Right by Sheldon Axler, 2nd ed or lat
University of Newcastle
School of Mathematical and Physical Sciences
MATH2320 - Linear Algebra
Workshop 6 (Week 7)
The textbook is Linear Algebra Done Right by Sheldon Axler, 2nd ed or later. This
Workshop covers Lecture 11 (8.1 Generalized Eigenvectors,
Questions which review material from Week 8 (Monday) and Week 9 (Friday):
1. Let V be a finite-dimensional inner-product space. Let U be a subspace of V , and (e1 , . . . , em )
an orthonormal basis of U . Recall that the orthogonal projection of V onto U
Recall: a Vector Space V = (S, +, ) comprises a set S of objects we call vectors, a field F (such as
the real numbers R or complex numbers C), an operation + such that the sum of any two vectors
u and v in S is another vector u + v in S, and another opera
Questions which review material from Week 2:
1. Let P3 (C) be the vector space of complex polynomials with degree less than or equal to 3.
(a) Show that the list of vectors B = x 1, (x 1)2 is linearly independent.
(b) Show that B does not span P3 (C) by g
Question which reviews material from Week 7 (Friday):
Recall that if V is a vector space over a field F, then an inner product on V is a function that
takes each ordered pair (v, w) of elements of V to a number hv, wi F, and has the following
properties:
Questions which review material from Week 4:
1. Consider the operator T L(P2 (R) defined by
T (p(x) = p(x) + xp0 (x).
(a) Find null T and use this to conclude that T must be invertible.
(b) Define the one-dimensional subspaces
U1 = cfw_a1 : a R,
U2 = cfw_
Questions which review material from Week 11:
1. Let T L(R4 ) have the matrix representation
1 1
1 1
1 1 1 1
M(T ) =
1 1 1 1 ,
1 1 1
1
with respect to the standard basis.
(a) If T self-adjoint? Is T normal? Explain your answer.
(b) Let U = span (1, 1, 0
Questions which review material from Week 5:
1. Consider the operator T L(R2 ) defined by
T (x, y) = (2x + 3y, 4y).
(a) Show that T has an upper-triangular matrix representation with respect to the standard
basis B = (1, 0), (0, 1) of R2 . Hence state the
Questions which review material from Week 6:
1. Consider the operator T L(C4 ), whose matrix
basis B of C4 is:
2
0
M(T, B) =
0
0
representation with respect to the standard
0 1 2
3 3 4
.
0 2 0
0 0 3
Define the vectors v1 = (1, 0, 0, 0), v2 = (0, 3, 1, 0)
Questions which review material from Week 10:
1. Let D L(P1 (R) be the differentiation operator on polynomials with real coefficients and
degree at most 1, and let S L(P1 (R) be defined by
S(c + dx) = 3cx.
Equip P1 (R) with the inner product defined by
1
University of Newcastle
School of Mathematical and Physical Sciences
MATH2320 - Linear Algebra
Workshop 4 (Week 5)
The textbook is Linear Algebra Done Right by Sheldon Axler, 2nd ed or later. This
Workshop covers Lecture 7 (3.4 Invertibility, 5.1 Invarian
AP Macroeconomics Review
Calendar:
May 14th,15th 2015
12:30 p.m. Macro
7:30 a.m. Micro
Topics and percentages
8-12% Basic Economic Concepts
12-16% Measurement of Economic Performance
10-15% National Income and Price Determination
15-20% Financial Sect