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a)if A is 6x8 what is the smallest possible dimension of N(A) ? the largest possible dim of N(A) b) if A is 6x4 what is smallest possible dim of N(A) ? the largest possible dim of R(A) ? smallest possible dim of N(At )? c) if A is 4x7 and rank (A) =3 what is dim N(A) ? does R(A) = R^3? why or why not? Solution a) There are 6 rows, and 8 columns, so each row could be independent. If so, they could all map to independent vectors, so the minimal dimension is 8-6=2. All vectors could map to 0, so the maximum dimension is 8. b) Since there are 6 rows.. if they are all independent, N(A)=0. The range space can be at most dim 4. For N(At) the minimum dimension is 2 (as in part a) c) We know that dim = rank + null, so 7 = 3 + N(A) so N(A)=4 R(A) is not R3... R(A) lies in R7 and is a subspace of that. There is, however, a bijection between R(A) and R3..

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saket.ppt

saket.ppt

maths 12th.pdf

maths 12th.pdf

Algebraic Properties of Matrix Operations

Algebraic Properties of Matrix Operations

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saket.ppt

This document discusses methods for finding the rank of a matrix. It begins by introducing the concept of linear independence and dependence of vectors. It then explains that the rank of a matrix is the maximum number of linearly independent columns. Two methods are described for determining the rank: using the determinant, and reducing the matrix to row echelon form. An example applying each method is provided. The document concludes by thanking the audience.

maths 12th.pdf

This document contains a sample question paper for Class XII Mathematics. It has 5 sections (A-E). Section A contains 18 multiple choice questions and 2 assertion-reason questions worth 1 mark each. Section B has 5 very short answer questions worth 2 marks each. Section C contains 6 short answer questions worth 3 marks each. Section D has 4 long answer questions worth 5 marks each. Section E contains 3 case study/passage based questions worth 4 marks each with internal subparts. The document provides sample questions on topics including trigonometry, calculus, matrices, probability, linear programming and more.

Algebraic Properties of Matrix Operations

Algebraic Properties of Matrix Operations
The m x n matrix with all entries of zero is denoted by 푶_풎풏 , for a matrix A of size m x n, we have:

FMS_MCQ_QUESTION_BANK.pdf

1. This document contains a question bank on the topic of metrics spaces and topology. It includes 11 topics with multiple choice questions on concepts like metric spaces, open and closed sets, topological spaces, and examples of metric spaces like the real line and plane.
2. The questions assess understanding of fundamental topological concepts such as metrics, open and closed sets, topological spaces, and examples of specific topological spaces.
3. The document is a study guide containing practice questions to test comprehension of foundational topics in metric spaces and general topology.

Eighan values and diagonalization

This document discusses eigenvalues and diagonalization of matrices. Some key points:
- Eigenvalues are values that satisfy the equation AX = λX, where X is a non-zero eigenvector. The eigenspace associated with λ contains all eigenvectors for that eigenvalue.
- The characteristic polynomial of a matrix A is defined as det(xI - A). The eigenvalues of A are the roots of its characteristic polynomial.
- Similar matrices have the same eigenvalues, determinant, rank, trace, and characteristic polynomial. Two matrices are similar if one can be obtained from the other by conjugation via an invertible matrix.
- The trace of a matrix is the sum of its diagonal entries

Relation and function_xii

The document discusses relations and functions. It defines relations as subsets of Cartesian products of sets and describes how to classify relations as reflexive, symmetric, transitive, or an equivalence relation. It also defines functions, including their domain, codomain, and range. It describes how to classify functions as injective, surjective, or bijective. Examples are provided to illustrate these concepts of relations and functions.

Independence, basis and dimension

This document discusses linear independence, basis, and dimension in linear algebra. It defines linear independence as vectors being linearly independent if the only solution that produces the zero vector is the trivial solution with all coefficients equal to zero. A basis is defined as a set of linearly independent vectors that span the vector space. The dimension of a vector space is the number of vectors in any basis of that space. The dimensions of the four fundamental subspaces (row space, column space, nullspace, and left nullspace) of a matrix are defined in terms of the rank of the matrix.

Chapter 4: Vector Spaces - Part 4/Slides By Pearson

This document provides information about finding bases and dimensions of subspaces related to matrices. It defines the row space and column space of a matrix, and explains that the row rank and column rank of a matrix are equal. The dimension of the null space gives the number of free variables, while the column rank equals the number of pivot columns. Examples show how to find bases for the row space, column space, and null space of a matrix by row reducing to echelon form.

ArrayBasics.ppt

Arrays in Matlab can be rectangular arrangements of numbers or other objects. A key array concept is that entries are stored sequentially in memory. Common array operations include creating arrays using functions like ones(), zeros(), rand(), accessing/assigning elements using indexes, and reshaping arrays without changing the underlying data. Plotting functions like plot() allow visualizing relationships between data vectors.

Mathematics JEE quick revision notes pdf

The document provides information about sets, relations, and functions in mathematics:
- A set is a collection of distinct objects, called elements or members. Sets are represented using curly brackets and elements are separated by commas. There are finite and infinite sets. Operations on sets include union, intersection, complement, difference, and power set.
- A relation from a set A to a set B is a subset of the Cartesian product A × B. The domain is the set of first elements in the relation and the range is the set of second elements.
- A function from a set A to a set B is a special type of relation where each element of A is mapped to exactly one element of B.

Linear Algebra Assignment help

This document provides contact information for math assignment help, including a phone number and email address. It then presents solutions to several problems from a linear algebra textbook. The problems cover topics like writing a quadratic form as a sum of squares, finding the closest line and plane of best fit to a set of points, orthonormal vectors, and determinants. Solutions are provided in mathematical notation and include working steps.

Eigen value and vectors

This document summarizes key concepts regarding eigenvalues and eigenvectors of matrices:
- Eigenvalues are scalars such that there exist non-zero eigenvectors satisfying Ax = λx.
- The characteristic equation states that λ is an eigenvalue if and only if it satisfies det(A - λI) = 0.
- A matrix is diagonalizable if it can be written as A = PDP-1, where D is a diagonal matrix of eigenvalues and P is a matrix of corresponding eigenvectors. Diagonalizable matrices can easily compute powers by raising the eigenvalues to powers.

Circunfêrencia 1

The document contains 15 multiple choice questions related to circles (circunferências) in the plane. Some key details assessed include:
1) Equations of lines parallel to a given line that intersect a circle and form equal chord lengths.
2) Finding which values satisfy an equation relating a line intersecting a circle.
3) Analyzing statements about triangles, lines, and circles.
4) Calculating the product of symmetrics and conjugates of complex numbers within a given set.
5) Determining the range of a chord length measured by a line intersecting a circle.
The questions cover topics such as parallel lines, secants, tangents, intersections, radii,

Unicamp 2015 - aberta

This document contains 6 math problems from a 2015 exam:
1) Find the area function A(t) of a triangle on a line and where it intersects for t values from 0 to 4. Also find the value of k such that a function g(x) intersects the line at only one point.
2) Show an expression is an integer and find values of x such that another expression equals 52.
3) Find integer solutions to an inequality of two affine functions and find when two other functions are equal.
4) Find ratios of areas for a circle and sector with an angle of 60 degrees and when their radii are in a certain ratio.
5) Show a cubic polynomial has a

AN ALPHA -CUT OPERATION IN A TRANSPORTATION PROBLEM USING SYMMETRIC HEXAGONAL...

In this paper we introduce a new operation on alpha cut for a symmetric hexagonal fuzzy numbers. We considered a transportation problem where the fuzzy demand and supply are in symmetric hexagonal fuzzy numbers and the minimum optimal cost is arrived .Transportation problems have various purposes in logistics and supply process for reducing the transportation cost’s The advantages of the proposed alpha
cut operations over existing methods is simpler and computationally more efficient in day to day applications.

Math

The document discusses properties of lattices and proofs related to lattices. It contains 6 questions with solutions. Question 1 defines sets A, B, C and verifies their intersections. Question 2 proves an identity related to general progressions. Question 3 determines the number of possible two-digit numbers that can be formed with and without repetition of digits. Question 4 solves a recurrence relation. Question 5 checks if given sets of vectors are linearly dependent or independent. Question 6 proves that an algebraic lattice forms a partially ordered set.

Matrix

A matrix is a rectangular array of numbers arranged in rows and columns. There are several types of matrices including square, rectangular, diagonal, identity, and triangular matrices. Operations that can be performed on matrices include addition, subtraction, multiplication by a scalar, and determining the transpose, determinant, and inverse of a matrix. A C program is shown that uses nested for loops to input and output the elements of a matrix.

saket.ppt

saket.ppt

maths 12th.pdf

maths 12th.pdf

Algebraic Properties of Matrix Operations

Algebraic Properties of Matrix Operations

FMS_MCQ_QUESTION_BANK.pdf

FMS_MCQ_QUESTION_BANK.pdf

Eighan values and diagonalization

Eighan values and diagonalization

Relation and function_xii

Relation and function_xii

Independence, basis and dimension

Independence, basis and dimension

Chapter 4: Vector Spaces - Part 4/Slides By Pearson

Chapter 4: Vector Spaces - Part 4/Slides By Pearson

ArrayBasics.ppt

ArrayBasics.ppt

Mathematics JEE quick revision notes pdf

Mathematics JEE quick revision notes pdf

Linear Algebra Assignment help

Linear Algebra Assignment help

Eigen value and vectors

Eigen value and vectors

Circunfêrencia 1

Circunfêrencia 1

Unicamp 2015 - aberta

Unicamp 2015 - aberta

AN ALPHA -CUT OPERATION IN A TRANSPORTATION PROBLEM USING SYMMETRIC HEXAGONAL...

AN ALPHA -CUT OPERATION IN A TRANSPORTATION PROBLEM USING SYMMETRIC HEXAGONAL...

Math

Math

Matrix

Matrix

A. Given the following information about the increase in revenue for.pdf

A. Given the following information about the increase in revenue for top companies x compared
to the pay CEO’s receive y.
x: 24 23 25 18 6 4 21 37 ( Percent for company)
y: 21 25 20 14 -4 19 15 30 ( Percent Salary increase for CEO)
Find the Sd.
Solution
standard deviation x,Sd= 9.9718 (answer) y,Sd =9.4472 (answer).

a. primary datab. explanatory datac. secondary datad. pilot da.pdf

a. primary data
b. explanatory data
c. secondary data
d. pilot data
e. preliminary data
Solution
1) Primary data is a type of information that is obtained directly from first-hand sources by
means of surveys, observation or experimentation. It is data that has not been previously
published and is derived from a new or original research study and collected at the source such
as in marketing.
2)Instatistics,exploratory data analysis (EDA)is an approach toanalyzingdata setsto summarize
their main characteristics, often with visual methods. Astatistical modelcan be used or not, but
primarily EDA is for seeing what the data can tell us beyond the formal modeling or hypothesis
testing task. Exploratory data analysis was promoted byJohn Tukeyto encourage statisticians to
explore the data, and possibly formulate hypotheses that could lead to new data collection and
experiments
3)
Secondary data is all the information collected for purposes other than the completion of a
research project and it.

A. the interval includes zero. B. the interval does NOT include ze.pdf

A. the interval includes zero.
B. the interval does NOT include zero.
C. the intervals are made at 95% Individual confidence level.
D. the intervals are made at 95% Familyconfidence level.
E. the intervals do overlap.
Solution
F. the interval does NOT include zero.
if there is significant difference then interval doesnt include 0 (x1-x2 is not equal to 0).

a. Suppose Z is Normally distributed (0,1). What value of z makes t.pdf

a. Suppose Z is Normally distributed (0,1). What value of z* makes the following equation true?
P( -z* < Z < z* ) = 0.45.
b. What is the 75th percentile of the standard normal distribution?
Solution
P(-z-z)=1-P(Z<-z)=1-No(-z) No(-z)=1-No(z) P(-z z=0.6 b) P(Z.

A. Strong trend that indicates business growth. B. A lack of an ad.pdf

A. Strong trend that indicates business growth.
B. A lack of an adequate number of data observations.
C. Significant unexplained business cycles.
D. Residuals with all positive signs.What is the typical cause of positive serial correlation in
business data?
Solution
D. Residuals with all positive signs.
Serial correlation occurs in time-series studies when the errors associated with a given time
period carry over into future time periods..

a. Operationalizationb. Data entryc. Editingd. Measuremente..pdf

a. Operationalization
b. Data entry
c. Editing
d. Measurement
e. Coding
I believe the answer is \'e\' Coding, but would appreciate some feedback. Please explain your
reasoning in clear and easily understood language.
Solution
e. Coding
So that reponse can be hidden from people. To keep answers confidential.

A. No since the D-W statistics is below 2.5. B. No since the VIFs .pdf

A. No since the D-W statistics is below 2.5.
B. No since the VIFs are below 2.5.
C. Yes since the F value is very high at 745.9.
D. No since the constant term is significant.
E. Yes since the DW statistic is below the lower table value for this model.Does the best
regression model have significant multicollinearity?
Solution
Option B
If the VIF is equal to 1 there is no multicollinearity, but if the VIF is greater than 1, the
independent variables may be moderately correlated. A VIF between 1 to 2.5 represents
moderately correlated or insignificantly correlated. A VIF between 5 and 10 indicates high
correlation (multicollinearity)..

A. have become more pronounced than in previous periods. B. have b.pdf

A. have become more pronounced than in previous periods.
B. have become more frequent than in previous periods.
C. have become less severe than in previous periods.
D. have not changed in severity or length in spite of government actions.Due to monetary policy
and fiscal policy intervention by the Federal Government since the 1950s business cycles
Solution
Option C: have become less severe than in previous periods.
Recessions in the United States have become noticeably less frequent and severe since 1950s.
There were three recessions between 1973 and 1982, but, then the 1982 trough was followed by
eight years of uninterrupted expansion. The 1980 recession lasted just six months, while the 1981
recession lasted sixteen months..

a. Explain the evolution of corporate governance. What problems deve.pdf

a. Explain the evolution of corporate governance. What problems developed? What are the
current trends?
b. What are the major criticisms of boards of directors? Which single criticism do you find to be
the most important? Why?
Solution
a. Evolution of corporate governance
Ever since the concept of corporate entity was recognized, corporate governance in various
manifestations has been in existence.
b. Major criticisms of boards of directors
The major criticisms of board of directors are as follows,
Lack Of Diversity
Boards of directors have long been criticized for having low numbers of female directors,
especially when their constituencies have large numbers of women. In 2012, ConocoPhillips and
Facebook were two public companies that added a woman after criticism for solely having white
males on their boards. Companies with board diversity have proven to be better performers than
companies without board diversity. As a board director, you can support diversity by sourcing
and mentoring female and minority professionals who can make valuable contributions to your
organization\'s work.
Lack Of Expertise
Board directors who are not qualified to make decisions related to their roles are criticized once
the company goes in a detrimental direction. In 2013, JPMorgan lost two longtime directors
because of decisions they made as members of the board\'s risk committee, despite not having
backgrounds in risk management. As a board director, be confident in the contributions you
make to the board and the company. Work in committees in which you have qualified
perspective instead of using board committees as a training ground to acquire new skills.
Non-profit Board
Weak fundraising, short-sighted strategy and misunderstanding their roles are major criticisms of
non-profit boards of directors. They have been chastised for not being stronger fundraisers and
being reactive at resolving operational issues instead of creating a long-term strategy for meeting
the mission of the non-profit. These relate to not fully understanding the role of a board director
versus non-profit executive director and staff roles. You can mitigate these issues by
understanding your job description as a non-profit board director, remaining up-to-date on
industry and organization trends for educated strategy development and committing to
fundraising as well as encouraging your colleagues to do the same.
Among these the most important criticism is Lack of expertise because it hampers the company
as a whole..

A. Describe an organizations various stakeholders and their differ.pdf

A. Describe an organization\'s various stakeholders and their different interests (3 principal types
and the stakeholders under each type)
B. Under what condition can the firm most easily satisfy all stakeholders?
C. If the firm cannot satisfy all stakeholders, which ones must it satisfy in order to survive?
Solution
A stakeholder of a company is an individual or/ and a group who may affect or be affected by the
actions of a business. The concept was first introduced in 1963 memorandum in the Stanford
Research Institute. It defined the stakeholders as \"those groups minus whose support the
organization will cease to exist. \"
In the latter decades of the 20th century, the word \"stakeholder\" is commonly used to refer to a
person or group that has a legitimate interest in a project or in an entity. In talking about the
decision-making process for institutions.

A. Characterized by a family of distibution, where each distibution .pdf

This document discusses a family of distributions characterized by two degrees of freedom, with the distribution becoming more symmetric as the numerator and denominator degrees of freedom increase. The distribution is positively skewed with values ranging from 0 to infinity, and the degrees of freedom have a Poisson distribution.

a. An economy is initially at the natural level of output. There is .pdf

a. An economy is initially at the natural level of output. There is an increase in government
spending. Use the IS
Solution
B.) Impact of Short Run and Long Run results on Inflation Bias and Other Problems of Policy
Formulation
Problems of policy formulation:
Inflation bias.

a. All internal auditors need at least a baseline level of IT audit-.pdf

a. All internal auditors need at least a baseline level of IT audit-related expertise.
1. Identify six specific IT-related competencies (that is, knowledge and skills) that all entry-level
internal auditors should possess.
2. Discuss how a college student can begin to develop the knowledge and skills identified in
number 1. above.
b. Must all internal auditors have the level of IT audit-related expertise expected of an IT
auditor? Explain.
Solution
a)
1)
Six specific IT-related competencies are as follows:
Security adminstration
Access controls at net work
Operating system
Database and
Application levels
2)
They will get to knowon their engagement to internal audit.
b)
Yes, the internal auditors must have IT audit-related expertise for proper adminstration..

a. 2 b. 8.03 c. 8.24 d. 8.33 e. 8.42 f. 20 Find the Effect.pdf

a. 2% b. 8.03% c. 8.24% d. 8.33% e. 8.42% f. 20% Find the Effective Annual Yield (EAY) of an
investment that pays 8% compounded continuously.
Solution
EAY for interest rate r continously compounding = = e^r -1 = e^8% -1 = e^0.08 -
1 = 8.328 %.

a. 0.431b. 2.154c. 4.512d. 6.512e. 17.408I understand that.pdf

a. 0.431
b. 2.154
c. 4.512
d. 6.512
e. 17.408
I understand that you have to integrate the v(t) function, i just cant seem to integrate it... like at
all. so if you could keep it simple and not involve any inverse hyperbolic sine stuff etc and keep
it at Calc AB level. simple :) much appreciated
Solution
d. 6.512 The distance traveled is 2 + ?(³v1+t²) [from t = 0 to t = 3] = 2 + 4.51153....

A) What is the probability that A occursB)What is the probability.pdf

A) What is the probability that A occurs?
B)What is the probability that B2 occurs?
C)What is the probability that Ac and B4 occur?
d) What is the probability that A or B3 occurs?
e) Given that B2 has occurred, what is the probability that A occurs?
f) Given that A has occurred, what is the probability that B4 occurs?
PLEASE SHOW ALLL WORK!!!!
e) Given that B2 has occurred, what is the probability that A occurs?
f) Given that A has occurred, what is the probability that B4 occurs?
PLEASE SHOW ALLL WORK!!!! Consider the following joint probability table.
Solution
(a) P(A occurs) =0.1+0.09+0.17+0.09 =0.45
(b) P(B2 occurs) =0.09+0.21 =0.3
(c) P(Ac and B4 occur) =0.16
(d) P( A or B3 occurs) = P(A occurs) +P(B3 occurs) - P(A and B3 occur) = 0.45+0.17+0.09-0.17
=0.54
(e) P(A occurs | B2 has occurred) = P(A and B2 occurred) / P(B2 occurred)
=0.09/0.3 =0.3
(f) P( B4 occurs | A has occurred) = P(A and B4 occurred)/ P(A occurred)
=0.09/0.45
=0.2.

a)Write a brief summary ofAl-Kashicontributions in Algebra and T.pdf

Al-Kashi made significant contributions to algebra and trigonometry in the 15th century. He was the first to explicitly state the law of cosines, useful for triangulation. He also calculated pi more accurately in his famous Treatise on the Circumference completed in 1424.

a) What is the degree of vertex Q b) What is the degree o.pdf

a) What is the degree of vertex Q ?
b) What is the degree of vertex R ?
c) How many components does the graph have ?
Solution
a) OQ , QR , QT , QV as it is attached to 4 other vertices - degree - 4 b) QR ,RS
,RV it is attached to 3 vertices degree = 3 c) i did not get the meaning of component.

A. Given the following information about the increase in revenue for.pdf

A. Given the following information about the increase in revenue for.pdf

a. primary datab. explanatory datac. secondary datad. pilot da.pdf

a. primary datab. explanatory datac. secondary datad. pilot da.pdf

A. the interval includes zero. B. the interval does NOT include ze.pdf

A. the interval includes zero. B. the interval does NOT include ze.pdf

a. Suppose Z is Normally distributed (0,1). What value of z makes t.pdf

a. Suppose Z is Normally distributed (0,1). What value of z makes t.pdf

A. Strong trend that indicates business growth. B. A lack of an ad.pdf

A. Strong trend that indicates business growth. B. A lack of an ad.pdf

a. Operationalizationb. Data entryc. Editingd. Measuremente..pdf

a. Operationalizationb. Data entryc. Editingd. Measuremente..pdf

A. No since the D-W statistics is below 2.5. B. No since the VIFs .pdf

A. No since the D-W statistics is below 2.5. B. No since the VIFs .pdf

A. have become more pronounced than in previous periods. B. have b.pdf

A. have become more pronounced than in previous periods. B. have b.pdf

a. Explain the evolution of corporate governance. What problems deve.pdf

a. Explain the evolution of corporate governance. What problems deve.pdf

A. Describe an organizations various stakeholders and their differ.pdf

A. Describe an organizations various stakeholders and their differ.pdf

A. Characterized by a family of distibution, where each distibution .pdf

A. Characterized by a family of distibution, where each distibution .pdf

a. An economy is initially at the natural level of output. There is .pdf

a. An economy is initially at the natural level of output. There is .pdf

a. All internal auditors need at least a baseline level of IT audit-.pdf

a. All internal auditors need at least a baseline level of IT audit-.pdf

a. 2 b. 8.03 c. 8.24 d. 8.33 e. 8.42 f. 20 Find the Effect.pdf

a. 2 b. 8.03 c. 8.24 d. 8.33 e. 8.42 f. 20 Find the Effect.pdf

a. 0.431b. 2.154c. 4.512d. 6.512e. 17.408I understand that.pdf

a. 0.431b. 2.154c. 4.512d. 6.512e. 17.408I understand that.pdf

A) What is the probability that A occursB)What is the probability.pdf

A) What is the probability that A occursB)What is the probability.pdf

a)Write a brief summary ofAl-Kashicontributions in Algebra and T.pdf

a)Write a brief summary ofAl-Kashicontributions in Algebra and T.pdf

a) What is the degree of vertex Q b) What is the degree o.pdf

a) What is the degree of vertex Q b) What is the degree o.pdf

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A beginner’s guide to project reviews - everything you wanted to know but wer...

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APM event held on 9 July in Bristol.
Speaker: Roy Millard
The SWWE Regional Network were very pleased to welcome back to Bristol Roy Millard, of APM’s Assurance Interest Group on 9 July 2024, to talk about project reviews and hopefully answer all your questions.
Roy outlined his extensive career and his experience in setting up the APM’s Assurance Specific Interest Group, as they were known then.
Using Mentimeter, he asked a number of questions of the audience about their experience of project reviews and what they wanted to know.
Roy discussed what a project review was and examined a number of definitions, including APM’s Bok: “Project reviews take place throughout the project life cycle to check the likely or actual achievement of the objectives specified in the project management plan”
Why do we do project reviews? Different stakeholders will have different views about this, but usually it is about providing confidence that the project will deliver the expected outputs and benefits, that it is under control.
There are many types of project reviews, including peer reviews, internal audit, National Audit Office, IPA, etc.
Roy discussed the principles behind the Three Lines of Defence Model:, First line looks at management controls, policies, procedures, Second line at compliance, such as Gate reviews, QA, to check that controls are being followed, and third Line is independent external reviews for the organisations Board, such as Internal Audit or NAO audit.
Factors which affect project reviews include the scope, level of independence, customer of the review, team composition and time.
Project Audits are a special type of project review. They are generally more independent, formal with clear processes and audit trails, with a greater emphasis on compliance. Project reviews are generally more flexible and informal, but should be evidence based and have some level of independence.
Roy looked at 2 examples of where reviews went wrong, London Underground Sub-Surface Upgrade signalling contract, and London’s Garden Bridge. The former had poor 3 lines of defence, no internal audit and weak procurement skills, the latter was a Boris Johnson vanity project with no proper governance due to Johnson’s pressure and interference.
Roy discussed the principles of assurance reviews from APM’s Guide to Integrated Assurance (Free to Members), which include: independence, accountability, risk based, and impact, etc
Human factors are important in project reviews. The skills and knowledge of the review team, building trust with the project team to avoid defensiveness, body language, and team dynamics, which can only be assessed face to face, active listening, flexibility and objectively.
Click here for further content: https://www.apm.org.uk/news/a-beginner-s-guide-to-project-reviews-everything-you-wanted-to-know-but-were-too-afraid-to-ask/SD_Integrating 21st Century Skills in Classroom-based Assessment.pptx

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Codeavour 5.0 International Impact Report - The Biggest International AI, Cod...

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Unlocking potential across borders! 🌍✨ Discover the transformative journey of Codeavour 5.0 International, where young innovators from over 60 countries converged to pioneer solutions in AI, Coding, Robotics, and AR-VR. Through hands-on learning and mentorship, 57 teams emerged victorious, showcasing projects aligned with UN SDGs. 🚀
Codeavour 5.0 International empowered students from 800 schools worldwide to tackle pressing global challenges, from bustling cities to remote villages. With participation exceeding 5,000 students, this year's competition fostered creativity and critical thinking among the next generation of changemakers. Projects ranged from AI-driven healthcare innovations to sustainable agriculture solutions, each addressing local and global issues with technological prowess.
The journey began with a collective vision to harness technology for social good, as students collaborated across continents, guided by mentors and educators dedicated to nurturing their potential. Witnessing the impact firsthand, teams hailing from diverse backgrounds united to code for a better future, demonstrating the power of innovation in driving positive change.
As Codeavour continues to expand its global footprint, it not only celebrates technological innovation but also cultivates a spirit of collaboration and compassion. These young minds are not just coding; they are reshaping our world with creativity and resilience, laying the groundwork for a sustainable and inclusive future. Together, they inspire us to believe in the limitless possibilities of innovation and the profound impact of young voices united by a common goal.
Read the full impact report to learn more about the Codeavour 5.0 International.BÀI TẬP BỔ TRỢ 4 KỸ NĂNG TIẾNG ANH LỚP 12 - GLOBAL SUCCESS - FORM MỚI 2025 - ...

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- 1. a)if A is 6x8 what is the smallest possible dimension of N(A) ? the largest possible dim of N(A) b) if A is 6x4 what is smallest possible dim of N(A) ? the largest possible dim of R(A) ? smallest possible dim of N(At )? c) if A is 4x7 and rank (A) =3 what is dim N(A) ? does R(A) = R^3? why or why not? Solution a) There are 6 rows, and 8 columns, so each row could be independent. If so, they could all map to independent vectors, so the minimal dimension is 8-6=2. All vectors could map to 0, so the maximum dimension is 8. b) Since there are 6 rows.. if they are all independent, N(A)=0. The range space can be at most dim 4. For N(At) the minimum dimension is 2 (as in part a) c) We know that dim = rank + null, so 7 = 3 + N(A) so N(A)=4 R(A) is not R3... R(A) lies in R7 and is a subspace of that. There is, however, a bijection between R(A) and R3.