This document provides a lesson on matrix inverses and solving systems of equations using inverse matrices. It begins with examples of determining whether two matrices are inverses of each other and finding the inverse of a given matrix. It then explains how to use inverse matrices to solve systems of equations by writing the system as a matrix equation and multiplying both sides by the inverse. Examples are provided to demonstrate solving systems using inverse matrices and decoding encoded messages using a given encoding matrix.
It contains the basics of matrix which includes matrix definition,types of matrices,operations on matrices,transpose of matrix,symmetric and skew symmetric matrix,invertible matrix,
application of matrix.
It contains the basics of matrix which includes matrix definition,types of matrices,operations on matrices,transpose of matrix,symmetric and skew symmetric matrix,invertible matrix,
application of matrix.
Securing your Kubernetes cluster_ a step-by-step guide to success !KatiaHIMEUR1
Today, after several years of existence, an extremely active community and an ultra-dynamic ecosystem, Kubernetes has established itself as the de facto standard in container orchestration. Thanks to a wide range of managed services, it has never been so easy to set up a ready-to-use Kubernetes cluster.
However, this ease of use means that the subject of security in Kubernetes is often left for later, or even neglected. This exposes companies to significant risks.
In this talk, I'll show you step-by-step how to secure your Kubernetes cluster for greater peace of mind and reliability.
Essentials of Automations: Optimizing FME Workflows with ParametersSafe Software
Are you looking to streamline your workflows and boost your projects’ efficiency? Do you find yourself searching for ways to add flexibility and control over your FME workflows? If so, you’re in the right place.
Join us for an insightful dive into the world of FME parameters, a critical element in optimizing workflow efficiency. This webinar marks the beginning of our three-part “Essentials of Automation” series. This first webinar is designed to equip you with the knowledge and skills to utilize parameters effectively: enhancing the flexibility, maintainability, and user control of your FME projects.
Here’s what you’ll gain:
- Essentials of FME Parameters: Understand the pivotal role of parameters, including Reader/Writer, Transformer, User, and FME Flow categories. Discover how they are the key to unlocking automation and optimization within your workflows.
- Practical Applications in FME Form: Delve into key user parameter types including choice, connections, and file URLs. Allow users to control how a workflow runs, making your workflows more reusable. Learn to import values and deliver the best user experience for your workflows while enhancing accuracy.
- Optimization Strategies in FME Flow: Explore the creation and strategic deployment of parameters in FME Flow, including the use of deployment and geometry parameters, to maximize workflow efficiency.
- Pro Tips for Success: Gain insights on parameterizing connections and leveraging new features like Conditional Visibility for clarity and simplicity.
We’ll wrap up with a glimpse into future webinars, followed by a Q&A session to address your specific questions surrounding this topic.
Don’t miss this opportunity to elevate your FME expertise and drive your projects to new heights of efficiency.
State of ICS and IoT Cyber Threat Landscape Report 2024 previewPrayukth K V
The IoT and OT threat landscape report has been prepared by the Threat Research Team at Sectrio using data from Sectrio, cyber threat intelligence farming facilities spread across over 85 cities around the world. In addition, Sectrio also runs AI-based advanced threat and payload engagement facilities that serve as sinks to attract and engage sophisticated threat actors, and newer malware including new variants and latent threats that are at an earlier stage of development.
The latest edition of the OT/ICS and IoT security Threat Landscape Report 2024 also covers:
State of global ICS asset and network exposure
Sectoral targets and attacks as well as the cost of ransom
Global APT activity, AI usage, actor and tactic profiles, and implications
Rise in volumes of AI-powered cyberattacks
Major cyber events in 2024
Malware and malicious payload trends
Cyberattack types and targets
Vulnerability exploit attempts on CVEs
Attacks on counties – USA
Expansion of bot farms – how, where, and why
In-depth analysis of the cyber threat landscape across North America, South America, Europe, APAC, and the Middle East
Why are attacks on smart factories rising?
Cyber risk predictions
Axis of attacks – Europe
Systemic attacks in the Middle East
Download the full report from here:
https://sectrio.com/resources/ot-threat-landscape-reports/sectrio-releases-ot-ics-and-iot-security-threat-landscape-report-2024/
UiPath Test Automation using UiPath Test Suite series, part 4DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 4. In this session, we will cover Test Manager overview along with SAP heatmap.
The UiPath Test Manager overview with SAP heatmap webinar offers a concise yet comprehensive exploration of the role of a Test Manager within SAP environments, coupled with the utilization of heatmaps for effective testing strategies.
Participants will gain insights into the responsibilities, challenges, and best practices associated with test management in SAP projects. Additionally, the webinar delves into the significance of heatmaps as a visual aid for identifying testing priorities, areas of risk, and resource allocation within SAP landscapes. Through this session, attendees can expect to enhance their understanding of test management principles while learning practical approaches to optimize testing processes in SAP environments using heatmap visualization techniques
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3. Optimization of testing processes
4. Demo
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Execution from the test manager
Orchestrator execution result
Defect reporting
SAP heatmap example with demo
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A presentation about the usage and availability of Varnish on Kubernetes. This talk explores the capabilities of Varnish caching and shows how to use the Varnish Helm chart to deploy it to Kubernetes.
This presentation was delivered at K8SUG Singapore. See https://feryn.eu/presentations/accelerate-your-kubernetes-clusters-with-varnish-caching-k8sug-singapore-28-2024 for more details.
LF Energy Webinar: Electrical Grid Modelling and Simulation Through PowSyBl -...DanBrown980551
Do you want to learn how to model and simulate an electrical network from scratch in under an hour?
Then welcome to this PowSyBl workshop, hosted by Rte, the French Transmission System Operator (TSO)!
During the webinar, you will discover the PowSyBl ecosystem as well as handle and study an electrical network through an interactive Python notebook.
PowSyBl is an open source project hosted by LF Energy, which offers a comprehensive set of features for electrical grid modelling and simulation. Among other advanced features, PowSyBl provides:
- A fully editable and extendable library for grid component modelling;
- Visualization tools to display your network;
- Grid simulation tools, such as power flows, security analyses (with or without remedial actions) and sensitivity analyses;
The framework is mostly written in Java, with a Python binding so that Python developers can access PowSyBl functionalities as well.
What you will learn during the webinar:
- For beginners: discover PowSyBl's functionalities through a quick general presentation and the notebook, without needing any expert coding skills;
- For advanced developers: master the skills to efficiently apply PowSyBl functionalities to your real-world scenarios.
Epistemic Interaction - tuning interfaces to provide information for AI supportAlan Dix
Paper presented at SYNERGY workshop at AVI 2024, Genoa, Italy. 3rd June 2024
https://alandix.com/academic/papers/synergy2024-epistemic/
As machine learning integrates deeper into human-computer interactions, the concept of epistemic interaction emerges, aiming to refine these interactions to enhance system adaptability. This approach encourages minor, intentional adjustments in user behaviour to enrich the data available for system learning. This paper introduces epistemic interaction within the context of human-system communication, illustrating how deliberate interaction design can improve system understanding and adaptation. Through concrete examples, we demonstrate the potential of epistemic interaction to significantly advance human-computer interaction by leveraging intuitive human communication strategies to inform system design and functionality, offering a novel pathway for enriching user-system engagements.
Encryption in Microsoft 365 - ExpertsLive Netherlands 2024Albert Hoitingh
In this session I delve into the encryption technology used in Microsoft 365 and Microsoft Purview. Including the concepts of Customer Key and Double Key Encryption.
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Let me take this questions and provide you a short journey through existing deployment models and use cases for AI software. On practical examples, we discuss what cloud/on-premise strategy we may need for applying it to our own infrastructure to get it to work from an enterprise perspective. I want to give an overview about infrastructure requirements and technologies, what could be beneficial or limiting your AI use cases in an enterprise environment. An interactive Demo will give you some insides, what approaches I got already working for real.
Builder.ai Founder Sachin Dev Duggal's Strategic Approach to Create an Innova...Ramesh Iyer
In today's fast-changing business world, Companies that adapt and embrace new ideas often need help to keep up with the competition. However, fostering a culture of innovation takes much work. It takes vision, leadership and willingness to take risks in the right proportion. Sachin Dev Duggal, co-founder of Builder.ai, has perfected the art of this balance, creating a company culture where creativity and growth are nurtured at each stage.
5. A matrix can have an inverse only if it is a square
matrix. But not all square matrices have inverses. If
the product of the square matrix A and the square
matrix A–1 is the identity matrix I, then AA–1 = A–1 A =
I, and A–1 is the multiplicative inverse matrix of
A, or just the inverse of A.
7. Example 1A: Determining Whether Two Matrices Are Inverses
Determine whether the two given matrices are inverses.
The product is the identity matrix I, so
the matrices are inverses.
Example 1B: Determining Whether Two Matrices Are Inverses
Determine whether the two given matrices are inverses.
Neither product is I, so the matrices are
not inverses.
8. Check It Out! Example 1
Determine whether the given matrices are
inverses.
The product is the
identity matrix I, so the
matrices are inverses.
9. If the determinant is 0, is undefined. So a matrix with a determinant of 0
has no inverse. It is called a singular matrix.
Example 2A: Finding the Inverse of a Matrix
Find the inverse of the matrix if it is defined.
First, check that the determinant is nonzero.
4(1) – 2(3) = 4 – 6 = –2. The determinant is –2, so the matrix has an
inverse.
The inverse of is
10. Example 2A: Finding the Inverse of a Matrix
Find the inverse of the matrix if it is defined.
First, check that the determinant is nonzero.
4(1) – 2(3) = 4 – 6 = –2. The determinant is –2, so the matrix has an
inverse.
The inverse of is
11. Example 2B: Finding the Inverse of a Matrix
Find the inverse of the matrix if it is defined.
The determinant is, , so B has
no inverse.
12. Check It Out! Example 2
Find the inverse of , if it is defined.
First, check that the determinant is nonzero.
3(–2) – 3(2) = –6 – 6 = –12
The determinant is –12, so the matrix has an inverse.
13. You can use the inverse of a matrix to solve a system
of equations. This process is similar to solving an
equation such as 5x = 20 by multiplying
each side by , the multiplicative inverse of 5.
To solve systems of equations with the inverse, you
first write the matrix equation AX = B, where A is
the coefficient matrix, X is the variable matrix,
and B is the constant matrix.
15. To solve AX = B, multiply both sides by the inverse A-1.
A-1AX = A-1B
IX = A-1B The product of A-1 and A is I.
X = A-1B
16. Caution!
Matrix multiplication is not commutative, so it is
important to multiply by the inverse in the same
order on both sides of the equation. A–1 comes
first on each side.
17. Example 3: Solving Systems Using Inverse Matrices
Write the matrix equation for the system and solve.
Step 1 Set up the matrix equation.
A X = B
Write: coefficient matrix variable
matrix = constant matrix.
Step 2 Find the determinant.
The determinant of A is –6 – 25 = –31.
19. Check It Out! Example 3
Write the matrix equation for and solve.
Step 1 Set up the matrix equation.
A X = B
Step 2 Find the determinant.
The determinant of A is 3 – 2 = 1.
20. Check It Out! Example 3 Continued
Step 3 Find A-1.
X = A-1 B
Multiply.
The solution is (3, 1).
22. 1 Understand the Problem
The answer will be the words of the
message, uncoded.
List the important information:
• The encoding matrix is E.
• The encoder used M as the message matrix, with
letters written as the integers 0 to 26, and then
used EM to create the two-row code matrix C.
23. 2 Make a Plan
Because EM = C, you can use M = E-1C to
decode the message into numbers and then
convert the numbers to letters.
• Multiply E-1 by C to get M, the message
written as numbers.
• Use the letter equivalents for the numbers
in order to write the message as words so
that you can read it.
24. 3 Solve
Use a calculator to find E-1.
Multiply E-1 by C.
13 = M, and so on
M A T H _ I
S _ B E S T
The message in words is “Math is best.”
25. 4 Look Back
You can verify by multiplying E by M to see
that the decoding was correct. If the math
had been done incorrectly, getting a
different message that made sense would
have been very unlikely.
26. Check It Out! Example 4
Use the encoding matrix to decode
this message .
27. 1 Understand the Problem
The answer will be the words of the
message, uncoded.
List the important information:
• The encoding matrix is E.
• The encoder used M as the message
matrix, with letters written as the integers 0 to
26, and then used EM to create the two-row
code matrix C.
28. 2 Make a Plan
Because EM = C, you can use M = E-1C to
decode the message into numbers and then
convert the numbers to letters.
• Multiply E-1 by C to get M, the message
written as numbers.
• Use the letter equivalents for the numbers in
order to write the message as words so that
you can read it.
29. 3 Solve
Use a calculator to find E-1.
Multiply E-1 by C.
18 = S, and so on
S M A R T Y
_ P A N T S
The message in words is “smarty pants.”
30. Lesson Quiz: Part I
1. Determine whether and are
inverses.
yes
2. Find the inverse of , if it exists.
31. Lesson Quiz: Part II
Write the matrix equation and solve.
3.
4. Decode using .
"Find the inverse."