Explain why the columns of an nxn matrix A are linearly independent when A is invertible.
Choose the correct answer below.
A. If A is invertible, then A has an inverse matrix A¹. Since A * A ^ - 1 = I A must have linearly independent columns.
B. If A is invertible, then for all x there is a b such that Ax = b. Since x = 0 is a solution of Ax = 0 the columns of A must be linearly independent.
C. If A is invertible, then the equation Ax = 0 has the unique solution x = 0 Since Ax = 0 has only the trivial solution, the columns of A must be linearly independent.
D. If A is invertible, then A has an inverse matrix A1. Since AA1=A1A, A must have linearly independent columns.
Answers
The columns of A must be linearly independent since the equation Ax=0 only has one solution if A is invertible, known as the trivial solution.
Which solution qualifies as trivial and nontrivial?There are some equations with simple structures that have answers that are trivial. They are less crucial, but because we must include them to be whole, we cannot omit them. The term "trivial solution" refers to a straightforward solution to an equation. Simple and straightforward answers are considered simple solutions. On the other hand, a solution that is difficult to find is considered non-trivial. According to the simple solution, each and every variable equals zero (i.e. the solution is the zero vector). The zero solution will always be the only one available if the system is homogenous and has one.To learn more about trivial solution, refer to:
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If A is invertible, then A has an inverse matrix A¹. Since A * A ^ - 1 = I A must have linearly independent columns is the statement that explains why the columns of an nxn matrix A are linearly independent when A is invertible.
What is an invertible matrix?A matrix that has an inverse is called an invertible matrix. Only square matrices can be invertible. A square matrix of size n x n is said to be invertible if and only if the determinant of the matrix is not equal to zero. Let's dive into the explanation:
1. If A is invertible, then A has an inverse matrix A¹. Since A * A ^ - 1 = I, we can assume that the columns of A must be linearly independent.
2. If the inverse of A, A¹, exists, we can write A¹A = I, where I is the identity matrix. Then, let's suppose that the columns of A are linearly dependent. This means that there exists a nonzero vector x such that Ax = 0.
3. Then, by multiplying both sides by A¹, we get x = A¹(0) = 0. This implies that the only solution to Ax = 0 is the trivial solution x = 0. This is contradictory to our assumption that the columns of A are linearly dependent.
Therefore, our assumption that the columns of A are linearly dependent was false, and thus the columns of an nxn matrix A are linearly independent when A is invertible.
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Related Questions
Each type of text has a purpose for the reader. If you were looking to research penguins what type of TEXT would you use?
A. textual
b. functional
c. recreational
d. digital
Answers
Each type of text has a purpose for the reader. If you were looking to research penguins, the type of TEXT that you would use option A. textual
What is the text purpose about?A text has a purpose for the reader, and if you are looking to research penguins, you would use a textual text. A textual text provides information, data or knowledge on a specific topic, and in this case, it would be about penguins.
Therefore, This type of text is usually used for educational or informative purposes. It can be found in academic journals, books, and online resources that are designed to inform and educate the reader.
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Discuss the evolution of file system data processing and how it is helpful to understanding of the data access limitations that databases attempt to over come
Answers
Answer:
in times before the use of computers, technologist invented computers to function on disk operating systems, each computer was built to run a single, proprietary application, which had complete and exclusive control of the entire machine. the introduction and use of computer systems that can simply run more than one application required a mechanism to ensure that applications did not write over each other's data. developers of Application addressed this problem by adopting a single standard for distinguishing disk sectors in use from those that were free by marking them accordingly.With the introduction of a file system, applications do not have any business with the physical storage medium
The evolution of the file system gave a single level of indirection between applications and the disk the file systems originated out of the need for multiple applications to share the same storage medium. the evolution has lead to the ckean removal of data redundancy, Ease of maintenance of database,Reduced storage costs,increase in Data integrity and privacy.
Explanation:
HELP!!! 100 points!!!
1. Imagine that you are a consultant who has been hired to give a brief presentation about the ethics of creating and using digital videos and photos. What are the three most important points that you would want to make in your presentation?
Answers
As a consultant tasked with giving a brief presentation about the ethics of creating and using digital videos and photos, I would emphasize the following three points:
The Points to be emphasizedRespect for individuals' privacy and consent: Digital videos and photos can easily be shared and circulated, potentially invading people's privacy and personal lives. It is essential to obtain explicit consent from all individuals involved, including those who are being recorded, photographed, or otherwise portrayed.
Honesty and accuracy: Digital media can be manipulated to alter the truth and deceive viewers. It is crucial to maintain honesty and accuracy in the creation and use of digital videos and photos. Any manipulation should be disclosed and labeled as such, and viewers should be able to distinguish between real and manipulated content.
Responsible use and distribution: Digital videos and photos can have significant impacts on individuals and society, including spreading misinformation or causing harm. It is important to be mindful of the potential consequences and use and distribute digital media responsibly and ethically, avoiding harmful or malicious content.
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As a consultant speaking about the ethics of creating and using digital videos and photos, the three most important points I would want to make in my presentation are:
Ethics is the branch of philosophy concerned with moral principles and values that govern behavior, decision-making, and interactions within society. It is concerned with what is right and wrong.
Respect for privacy: One of the most important ethical considerations when creating and using digital videos and photos is respect for privacy. It is important to obtain the consent of individuals before capturing their images or recording them, especially in situations where privacy is expected, such as in public restrooms, locker rooms, or bedrooms.
Authenticity and truthfulness: Digital videos and photos can be manipulated or edited to misrepresent reality. It is important to maintain authenticity and truthfulness by clearly labeling any edits or alterations and avoiding the use of deceptive techniques to create false impressions or messages.
Responsible use and distribution: Digital videos and photos can have a significant impact on individuals and communities. It is important to use and distribute these materials responsibly, avoiding the promotion of harmful or discriminatory messages, respecting the intellectual property rights of others, and considering the potential consequences of dissemination.
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Select the correct answer.
Which relationship is possible when two tables share the same primary key?
А.
one-to-one
B.
one-to-many
C.
many-to-one
D.
many-to-many
Answers
Answer:
Many-to-one
Explanation:
Many-to-one relationships is possible when two tables share the same primary key it is because one entity contains values that refer to another entity that has unique values. It often enforced by primary key relationships, and the relationships typically are between fact and dimension tables and between levels in a hierarchy.
1) Print person1's kids, apply the IncNumKids() function, and print again, outputting text as below. End each line with newline. Sample output for below program: Kids: 3 New baby, kids now: 4
#include
using namespace std;
class PersonInfo {
public:
void SetNumKids(int personsKids);
void IncNumKids();
int GetNumKids() const;
private:
int numKids;
};
void PersonInfo::SetNumKids(int personsKids) {
numKids = personsKids;
return;
}
void PersonInfo::IncNumKids() {
numKids = numKids + 1;
return;
}
int PersonInfo::GetNumKids() const {
return numKids;
}
int main() {
PersonInfo person1;
person1.SetNumKids(3);
this->numKids = numKids;
return 0;
}
Answers
To Print person1's kids, apply the IncNumKids() function, and print again, outputting text check the given code.
What is a function?A function is a piece of code that performs a specific task. It is callable and reusable multiple times. You can pass data to a function, and it can return data to you. Many programming languages include built-in functions that can be found in their libraries, but you can also write your own.
↓↓//code//↓↓
#include <iostream>
using namespace std;
class PersonInfo {
private:
int numKids;
public:
void setNumKids(int personsKids) {
numKids = personsKids;
return;
}
void incNumKids() {
numKids = numKids + 1;
return;
}
int getNumKids() {
return numKids;
}
};
int main() {
PersonInfo person1;
person1.setNumKids(3);
cout << "Kids: " << person1.getNumKids() << endl;
person1.incNumKids();
cout << "New baby, kids now: " << person1.getNumKids() << endl;
return 0;
}
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Assignment 6: Animation
Answers
Here is an example of an animated scene with a school-appropriate theme:
How to show the Programimport turtle
# Global variable to keep track of the score
score = 0
# Draw 5 circles
for i in range(5):
turtle.penup()
turtle.goto(i*30, 0)
turtle.pendown()
turtle.circle(20)
# Draw 5 polygons
for i in range(5):
turtle.penup()
turtle.goto(i*60, 50)
turtle.pendown()
for j in range(4):
turtle.forward(40)
turtle.right(90)
# Draw 5 lines
for i in range(5):
turtle.penup()
turtle.goto(i*90, -50)
turtle.pendown()
turtle.forward(100)
# Animate the scene
while True:
turtle.undo()
score += 1
turtle.write("Score: " + str(score), align="center",
font=("Arial", 14, "normal"))
This code creates an animated scene where five circles, five polygons, and five lines move across the screen, with the score increasing by 1 with each iteration of the while loop.
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outline the steps involved in changing the colour of a theme
Answers
Answer:
Right click on the desktop and click on personalize option and then click on window color. After that window color and appearance window appears. select a color scheme you want. Go to Appearance and personalization, click on theme and select any theme from the list and click on ok.
Henry wants to create a presentation for his clients. He wants to upload the presentation file directly to the Internet. Which presentation software can Henry use
Answers
Answer:
styrofoam and petroleum
Explanation:
Any Suggestions on what to do here? I already restarted my PC twice, cleared my browsing data, and rebooted the wifi network....
Answers
Answer:
if u r at school, then it might be blocked.
if not, get a vpn proxy.
you have just upgraded the memory in one of your network servers by adding two 4-gb ecc memory cards. before purchasing the new memory, you made sure that the modules fit in the memory slots (packaging) and the speed (memory frequency) was supported by the memory controller. what did you forget to check that would significantly impact the memory checking of your new ecc memory cards?
Answers
Answer:Whether or not the existing memory modules support
Explanation:
Mixing ECC and non-ECC memory would disable the error correction function on the new memory cards.
a small group of travelers is meeting inside an ancient building, and the travelers need access to the internet using their mobile devices. however, the group is in an area where wi-fi internet is not available and cellular coverage is intermittent. one of the travelers has an unlimited cellular data plan and a strong consistent signal. which of the following methods would most likely be implemented to provide internet service to the group?
Answers
The method that would most likely be implemented to provide internet service to the group is known as a Mobile hotspot.
What is the significance of mobile hotspots?The significance of a mobile hotspot is determined by the fact that it is a portable hotspot on your phone that lets you share your high-speed data to connect more devices to the internet in more places—all powered by our nationwide network.
According to the context of this question, the range of mobile hotspots may vary from 7-20 meters or sometimes more than that depending on the frequency level of the connection. It allows the mobile devices of other people to make connections with yours and enjoy high-speed data.
Therefore, the method that would most likely be implemented to provide internet service to the group is known as a Mobile hotspot.
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a DVD looks just like a CD, but it holds less information true or false
Answers
Answer:
False
Explanation:
A DVD can hold more information because it is basically a double sided CD where it gets information on both sides whereas on a CD, you only read one side. On CDs, people can put stuff like stickers or whatever on one side while the important side is uncovered.
What are the number of buttons on an average calculator?.
Answers
Answer:
56
Explanation:
There is 56
Which can be used to view a web page?
File viewer
Text editor
Web browser
WYSIWYG
Answers
The answer is C: web browser
so we use web browsers to look at web pages
hope this helped
-scav
How do i fix this? ((My computer is on))
Answers
Answer:
the picture is not clear. there could be many reasons of why this is happening. has your computer had any physical damage recently?
Answer:your computer had a Damage by u get it 101 Battery
and if u want to fix it go to laptop shop and tells him to fix this laptop
Explanation:
This isn't academic, but what do I do if HI-REZ won't let me sign into an existing account. “Something went wrong” keeps popping up when I type in the correct info
Answers
Answer:
contact their support
Explanation:
Which of the following is / are true about the gradient descent method? a. Gradient descent guarantees the best possible answer in one run of the algorithm b. It is an optimization algorithm that seeks to find the best parameters of a function c. Gradient descent works best for a convex optimization function d. Gradient descent requires the optimization function to be differentiable.
Answers
The following statement is true about the gradient descent method:
b. It is an optimization algorithm that seeks to find the best parameters of a function.
The gradient descent method is an iterative optimization algorithm used to find the optimal parameters or weights of a function. It is commonly used in machine learning and deep learning algorithms to minimize a cost function by adjusting the parameters in the direction of steepest descent. By iteratively updating the parameters based on the gradients of the cost function, the algorithm aims to converge to the optimal solution.
The other statements are not entirely true:
a. Gradient descent does not guarantee the best possible answer in one run of the algorithm. It depends on the specific problem and the convergence criteria used.
c. Gradient descent can work for both convex and non-convex optimization functions, although it may have challenges with local optima in non-convex cases.
d. Gradient descent requires the optimization function to be differentiable so that the gradients can be computed. Non-differentiable functions may require alternative optimization methods.
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You created a pivottable and changed some values in the dataset from which the pivottable was created. How does this affect the pivottable?.
Answers
When a user creates a pivot table and modifies the values in the source dataset, the pivot table is modified accordingly.
The pivot table immediately reflects the updated values from the source data set. It's an essential feature of a pivot table to react quickly to modifications in the source data set. A pivot table is a summary of data in a spreadsheet. It allows users to arrange and rearrange data in multiple ways, making it easier to understand and extract insights from the data.The power of a pivot table lies in its ability to dynamically group, summarize, and filter large datasets. This helps to easily compare, analyze, and present large volumes of data in a clear and concise format.
Pivot tables update immediately whenever changes are made in the source data set. This makes it possible to easily work with large datasets without having to manually update formulas or charts. Pivot tables can summarize large datasets in seconds, allowing users to quickly spot trends and patterns. This functionality is particularly useful when working with large datasets with many variables. Overall, pivot tables are an essential tool for anyone who needs to analyze large volumes of data.
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Arrange the sets from top to bottom so that each set is a subset of the set below it. IV. ▼ N = the set of natural numbers (positive integers) Il Q the set of rational numbers I. R-the set of real numbers . Ill. =the set of integers ▼
Answers
The sets can be arranged as follows: N ⊂ Z ⊂ Q ⊂ R, where each set is a subset of the set below it.
What is the correct arrangement of the sets N, Z, Q, and R in terms of subset relationships?
The sets can be arranged as follows from top to bottom, with each set being a subset of the set below it:
IV. N = the set of natural numbers (positive integers)
III. Z = the set of integers
II. Q = the set of rational numbers (fractions)
I. R = the set of real numbers
The natural numbers (N) are a subset of the integers (Z) because the integers include both positive and negative numbers.
The integers (Z) are a subset of the rational numbers (Q) because rational numbers include fractions. The rational numbers (Q) are a subset of the real numbers (R) because real numbers include both rational and irrational numbers.
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Importance of Dressmaking
1. Dressmakers are the ones who can can make impressive dresses out of any fabric. 2. They are great designers creating different trends. 3. Omnesmakers create different concepts and think out of the latest fashion, 4. They the ones who can make any dream gown or dress a reality. 5. Dressmakers help in enhancing their body assets and their flows
Answers
The importance of dressmaking is E. Dressmakers help in enhancing their body assets and their flows.
What is dressmaking?Making garments for women or girls is known as dressmaking. People who wear dresses might accentuate their physical assets and conceal their shortcomings. Like cosmetics, clothes are the essentials that can help a person highlight their best features and cover up any defects they want to keep hidden
A significant component of our civilization is clothing. People express themselves through their clothing choices. People who wear dresses might accentuate their physical assets and conceal their shortcomings. Like cosmetics, clothes are the essentials that can help a person highlight their best features and cover up any defects they want to keep hidden.
It should be noted that making dresses is an important job. In this case, the importance of dressmaking is that Dressmakers help in enhancing their body assets and their flows. Therefore, the correct option is E.
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what type of arithmetic operator has one argument to the left and another argument to the right of the operator?
Answers
A binary type of arithmetic operator has one argument to the left and another argument to the right of the operator, hence option A is correct.
What is the binary arithmetic operator?The standard arithmetic operations of addition, subtraction, multiplication, and division are all included in binary arithmetic.
The guidelines that govern these operations when they are carried out on binary numbers are presented in the following sections. An addition in the binary system works similarly to an addition in the decimal system.
Therefore, the binary type of arithmetic operator has one argument to the left and another argument to the right of the operator.
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The given question is incomplete so the most probable complete question is,
What type of arithmetic operator has one argument to the left and another argument to the right of the operator?
a) binary
b) unary
c) composite
d) complex
Which of the following is the term for the process to make sure the user has the right to access a system? O persistence O authentication
O commitment O permission
Answers
The term for the process to make sure the user has the right to access a system is called authentication. Option B is answer.
Authentication is the process of verifying the identity of a user or system. It is a security measure that ensures that only authorized users can access a particular system or resource. Authentication can be achieved using various methods, including passwords, biometric data, smart cards, or digital certificates. Once a user's identity is authenticated, they are granted access to the system or resource. Without authentication, unauthorized users could gain access to sensitive data and compromise the security of the system.
Option B, authentication, is the correct answer.
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What are some benefits that each computer system being used?
Answers
Answer:
Computerised accounting systems have numerous benefits to them and below are the top nine points as to why you should be using them with your business.
Automation. ...
Data Access. ...
Accuracy. ...
Reliability. ...
Speed. ...
Security. ...
Scalable. ...
Visuals.
Explanation:
hope this helps!
Answer:
Increase your productivity. ...
Connects you to the Internet. ...
Can store vast amounts of information and reduce waste. ...
Helps sort, organize, and search through information. ...
Get a better understanding of data. ...
Keeps you connected. ...
Help you learn and keep you informed. ...
Can make you money..
Explanation:
Robert is given a string that ends with a character or a number. he
has to check the length of the given string and append it to the end
in such a way that if the original string ends with a number then the
new string with the appended value must have the length of the
string as the last two characters. if the string ends with a character
then append the total length as the last character.
also, the number to be appended must be a single positive digit.
write a code to implement the given scenario.
input format
input consist of a string
output format
Answers
Robert should first identify the input and output formats, analyze the given string, perform the necessary operations based on the last Character, and then output the result using the determined format.
It seems like Robert is given a string that ends with either a character or a number, and he needs to process it using input and output formats.
Step 1: Identify the input format.
The input format could be a string provided by the user or a file containing the string. Robert should first understand how he will receive the string to process it accordingly.
Step 2: Analyze the string.
Robert needs to identify the last character of the string to determine whether it's a number or a character.
Step 3: Process the string based on the last character.
If the string ends with a number, Robert may perform a specific operation, such as doubling the number. If it ends with a character, he may perform a different operation, like converting the character to uppercase.
Step 4: Determine the output format.
Robert should know how the processed string should be displayed, whether it's printed on the screen, saved in a file, or returned as a variable in a program.
Step 5: Output the processed string.
Based on the output format, Robert will present the processed string accordingly. For example, if the output format is to print on the screen, he will use the appropriate command or function to display the result.
In summary, Robert should first identify the input and output formats, analyze the given string, perform the necessary operations based on the last character, and then output the result using the determined format.
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How are texting and instant messaging alike? I think its a A. They are forms of instant digital communication. B. Both must be done on a cell phone. C. Both must be done on a computer. D. Netiquette is not important when using either one.
Answers
Answer:
A
Explanation:
took quick check conexus
If you want to notify the sender, you need to select the "Message contains sensitive content. " condition for this rule. Error details:
Answers
If you want to notify the sender, you need to select the "Message that contains sensitive content. The condition for this rule is to notify the sender and take action that requires the message that contains a data classification predicate.
What do you mean by Sensitive content?Sensitive content may be defined as anything that may significantly provoke a sense of offense to a reader or user, particularly in relation to religion, race, gender, politics, sexuality, disability, or vulgar language.
According to the context of this question, the error details for this condition are provided to the sender in order to notify. This notification will definitely consist of all sorts of terms and conditions that are classified on the basis of data classification predicate.
Therefore, the condition for this rule is to notify the sender and take action that requires the message that contains a data classification predicate.
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Which java keyword must be present in the method signature of a method which can produce a checked exception?
Answers
The keyword 'throws' must be present in the method signature of a method which can produce a checked exception.
The 'throws' keyword is used to declare an exception which might be thrown by a method, allowing the programmer to handle the potential exception. A method signature may contain multiple 'throws' keywords if it may throw multiple exceptions.
For example, a method which reads a file from the system might throw a 'FileNotFoundException' if the file does not exist, and an 'IOException' if the file cannot be read for some reason. In this case, the method signature would look like this:
public void readFile() throws FileNotFoundException, IOException
This is necessary to inform the compiler that the method might throw an exception and the user of the method should handle it.
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matt is supervising the installation of redundant communications links in response to a finding during his organization's bia. what type of mitigation provision is matt overseeing?
Answers
The type of mitigation provision is matt overseeing is installing a redundant computer system.
What is mitigation provision?
A mitigation provision is a clause in a contract that requires one party to take reasonable steps to mitigate damages that may be caused by the other party's breach of the contract. Under the code's mitigation provisions, a bar to an assessment, credit, or refund imposed by the expiration of a statute of limitations or other rule of law can be waived.
Matt is overseeing the installation of redundant communications links in response to a finding during his organization's business impact analysis (BIA). This is an example of proactive mitigation, which is activity taken in advance of an incident to reduce its potential severity.
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What he name given to a cell with a green border around it?
Answers
Answer:
Active cell
Explanation:
I will assume this question is about spreadsheet programs (Microsoft Office Excel, for instance).
In Microsoft Office Excel, a cell that has border around it means that the cell is currently selected. The proper word for a selected cell is an active cell.
Hence, an active cell answers the question.
You will need an Excel Spreadsheet set up for doing Quantity Take- offs and summary estimate
sheets for the remainder of this course. You will require workbooks for the following:
Excavation and Earthwork
Concrete
Metals
Rough Wood Framing
Exterior Finishes
Interior Finishes
Summary of Estimate
You are required to set up your workbooks and a standard QTO, which you will submit
assignments on for the rest of the course. The QTO should have roughly the same heading as
the sample I have provided, but please make your own. You can be creative, impress me with
your knowledge of Excel. I have had some very professional examples of student work in the
past.
NOTE: The data is just for reference, you do not need to fill the data in, just create a QTO.
Build the columns, and you can label them, however you will find that you will need to adjust
these for different materials we will quantify.
Here are some examples of what they should look like:
Answers
We can see here that in order to create Excel Spreadsheet set up for doing Quantity Take- offs and summary estimate, here is a guide:
Set up the spreadsheet structureIdentify the required columnsEnter the item details: In each sheet, start entering the item details for quantity take-offs. What is Excel Spreadsheet?An Excel spreadsheet is a digital file created using Microsoft Excel, which is a widely used spreadsheet application. It consists of a grid of cells organized into rows and columns, where users can input and manipulate data, perform calculations, create charts and graphs, and analyze information.
Continuation:
4. Add additional columns to calculate the total cost for each item.
5. Create a new sheet where you will consolidate the information from all the category sheets to create a summary estimate.
6. Customize the appearance of your spreadsheet by adjusting font styles, cell formatting, and color schemes.
7. Double-check the entered quantities, unit costs, and calculations to ensure accuracy.
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