Category: Linear Algebra

The a-s-s-e-s-s-m-e-n-t will
Assignment
Please see the questions shown in the screenshot. I will send you all the info after being hired, eg PPTs, student access etc. Please send a draft in 12hrs -1 day time, day 2, and day 3 as well. + Will need to draft some questions to ask the teacher and revise base on feedback (Send bk ard in 1 day max)
https://drive.google.com/drive/folders/1xP-euq-Y9hSQpNl6I18vIPdsssaLQ1LU?usp=sharing

The a-s-s-e-s-s-m-e-n-t will
Assignment
Please see the questions shown in the screenshot. I will send you all the info after being hired, eg PPTs, student access etc. Please send a draft in 12hrs -1 day time, day 2, and day 3 as well. + Will need to draft some questions to ask the teacher and revise base on feedback (Send bk ard in 1 day max)
https://drive.google.com/drive/folders/1xP-euq-Y9hSQpNl6I18vIPdsssaLQ1LU?usp=sharing

It is an assignment in Algebra and Linear Equations. It is very easy, but I do not have time to solve it. I would be grateful if someone could help me.

It is an assignment in Algebra and Linear Equations. It is very easy, but I do not have time to solve it. I would be grateful if someone could help me.

In physics, linear algebra is an essential mathematical tool used to describe and analyze various physical systems and phenomena. Here’s how linear algebra is applied in different areas of physics:
1. Classical Mechanics:
Kinematics and Dynamics: Vectors are used to represent physical quantities like displacement, velocity, acceleration, and force. Linear transformations, represented by matrices, can describe rotations, translations, and other transformations in space.
Inertia Tensor: In rigid body dynamics, the inertia tensor (a matrix) is used to describe how the mass of a body is distributed relative to its rotational axes. The inertia tensor helps in calculating angular momentum and rotational kinetic energy.
2. Electromagnetism:
Electric and Magnetic Fields: The electric and magnetic fields are often represented as vector fields. Linear algebra helps in solving Maxwell’s equations, which describe how electric and magnetic fields propagate and interact.
Linear Systems of Equations: In circuits, systems of linear equations are used to solve for unknown currents and voltages in complex networks using methods like Kirchhoff’s laws.
3. Quantum Mechanics:
State Vectors and Operators: Quantum states are represented by vectors (state vectors) in a complex vector space known as Hilbert space. Observables like energy and momentum are represented by operators (which are linear transformations) acting on these vectors.
Eigenvalues and Eigenvectors: The possible outcomes of measurements in quantum mechanics correspond to the eigenvalues of operators, while the state of the system after measurement corresponds to the eigenvector associated with that eigenvalue.
Spin and Pauli Matrices: Spin is a fundamental property of particles, and it is described using Pauli matrices, which are 2×2 complex matrices used in the study of quantum spin systems.
4. Special and General Relativity:
Lorentz Transformations: In special relativity, Lorentz transformations are linear transformations that relate the coordinates of events as observed in different inertial frames of reference. These transformations are described using matrices.
Tensor Calculus: In general relativity, the curvature of spacetime and the distribution of matter and energy are described using tensors, which generalize the concept of matrices to higher dimensions.
5. Wave Mechanics:
Wave Equations: The propagation of waves (such as sound, light, or water waves) can be described by linear differential equations. Solutions to these equations often involve Fourier transforms, which rely on linear algebra.
Superposition Principle: The principle of superposition in wave mechanics states that the resultant wave is a linear combination of individual waves. This concept is rooted in linear algebra.
6. Statistical Mechanics:
Partition Functions and State Spaces: In statistical mechanics, the state of a system can be described as a vector in a high-dimensional space, and the behavior of the system can be analyzed using linear algebraic methods.
Markov Chains: In the study of stochastic processes, Markov chains can be represented using transition matrices, where linear algebra is used to find steady states and analyze the dynamics of the system.
7. Optics:
Polarization: The polarization of light can be described using vectors and matrices. The Jones calculus, for example, uses 2×2 matrices (Jones matrices) to describe the transformation of the polarization state of light as it passes through optical elements.
Linear algebra provides the mathematical foundation for many physical theories and is indispensable in solving physical problems, from simple vector operations to complex quantum mechanical systems. Understanding linear algebra is crucial for physicists and engineers in modeling and analyzing real-world physical systems.

With this assignment, students will provide a reflection of at least 600 words (or 3 pages double spaced) of how the knowledge, skills, or theories of this course have been applied or could be applied, in a practical manner to their current work environment. If you are not currently working, share times when you have or could observe these theories and knowledge that could be applied to an employment opportunity in your field of study.
Requirements:
Provide a 600-word (or 3 pages double spaced) minimum reflection
Use of proper APA formatting and citations. If supporting evidence from outside resources is used it must be properly cited
Share a personal connection that identifies specific knowledge and theories from the course
Demonstrate a connection to your current environment. If you are not employed, demonstrate a connection to your desired work environment
You should NOT provide an overview of the assignment in the course. The assignment asks that you reflect on how the knowledge and skills obtained through meeting course objectives were applied or could be applied in the workplace MUST BE 100% PLAGIARISM FREE

Overview
In this project, you will apply inference methods for means to test your hypotheses about the housing sales market for a region of the United States. You will use appropriate sampling and statistical methods.
Scenario
You have been hired by your regional real estate company to determine if your region’s housing prices and housing square footage are significantly different from those of the national market. The regional sales director has three questions that they want to see addressed in the report:
Are housing prices in your regional market lower than the national market average?
Is the square footage for homes in your region different than the average square footage for homes in the national market?
For your region, what is the range of values for the 95% confidence interval of square footage for homes in your market?
You are given a real estate data set that has houses listed for every county in the United States. In addition, you have been given national statistics and graphs that show the national averages for housing prices and square footage. Your job is to analyze the data, complete the statistical analyses, and provide a report to the regional sales director. You will do so by completing the Project Two Template located in the What to Submit area below.
Directions
Introduction
Region: Start by picking one region from the following list of regions:
West South Central, West North Central, East South Central, East North Central, Mid Atlantic
Purpose: What is the purpose of your analysis?
Sample: Define your sample. Take a random sample of 500 house sales for your region.Describe what is included in your sample (i.e., states, region, years or months).
Questions and type of test: For your selected sample, define two hypothesis questions (see the Scenario above) and the appropriate type of test for each. Address the following for each hypothesis:Describe the population parameter for the variable you are analyzing.
Describe your hypothesis in your own words.
Identify the hypothesis test you will use (1-Tail or 2-Tail).
Level of confidence: Discuss how you will use estimation and confidence intervals to help you solve the problem.
1-Tail Test
Hypothesis: Define your hypothesis.Define the population parameter.
Write null (Ho) and alternative (Ha) hypotheses. Note: For means, define a hypothesis that is less than the population parameter.
Specify your significance level.
Data analysis: Summarize your sample data using appropriate graphical displays and summary statistics and confirm assumptions have not been violated to complete this hypothesis test.Provide at least one histogram of your sample data.
In a table, provide summary statistics including sample size, mean, median, and standard deviation. Note: For quartiles 1 and 3, use the quartile function in Excel:
=QUARTILE([data range], [quartile number])
Summarize your sample data, describing the center, spread, and shape in comparison to the national information (under Supporting Materials, see the National Summary Statistics and Graphs House Listing Price by Region PDF). Note: For shape, think about the distribution: skewed or symmetric.
Check the conditions.Determine if the normal condition has been met.
Determine if there are any other conditions that you should check and whether they have been met. Note: Think about the central limit theorem and sampling methods.
Hypothesis test calculations: Complete hypothesis test calculations.Calculate the hypothesis statistics.Determine the appropriate test statistic (t). Note: This calculation is (mean – target)/standard error. In this case, the mean is your regional mean, and the target is the national mean.
Calculate the probability (p value). Note: This calculation is done with the T.DIST function in Excel:
=T.DIST([test statistic], [degree of freedom], True) The degree of freedom is calculated by subtracting 1 from your sample size.
Interpretation: Interpret your hypothesis test results using the p value method to reject or not reject the null hypothesis.Relate the p value and significance level.
Make the correct decision (reject or fail to reject).
Provide a conclusion in the context of your hypothesis.
2-Tail Test
Hypotheses: Define your hypothesis.Define the population parameter.
Write null and alternative hypotheses. Note: For means, define a hypothesis that is not equal to the population parameter.
State your significance level.
Data analysis: Summarize your sample data using appropriate graphical displays and summary statistics and confirm assumptions have not been violated to complete this hypothesis test.Provide at least one histogram of your sample data.
In a table, provide summary statistics including sample size, mean, median, and standard deviation. Note: For quartiles 1 and 3, use the quartile function in Excel:
=QUARTILE([data range], [quartile number])
Summarize your sample data, describing the center, spread, and shape in comparison to the national information. Note: For shape, think about the distribution: skewed or symmetric.
Check the assumptions.Determine if the normal condition has been met.
Determine if there are any other conditions that should be checked on and whether they have been met. Note: Think about the central limit theorem and sampling methods.
Hypothesis test calculations: Complete hypothesis test calculations.Calculate the hypothesis statistics.Determine the appropriate test statistic (t). Note: This calculation is (mean – target)/standard error. In this case, the mean is your regional mean, and the target is the national mean.]
Determine the probability (p value). Note: This calculation is done with the TDIST.2T function in Excel:
=T.DIST.2T([test statistic], [degree of freedom]) The degree of freedom is calculated by subtracting 1 from your sample size.
Interpretation: Interpret your hypothesis test results using the p value method to reject or not reject the null hypothesis.Compare the p value and significance level.
Make the correct decision (reject or fail to reject).
Provide a conclusion in the context of your hypothesis.
Comparison of the test results: Revisit Question 3 from the Scenario section: For your region, what is the range of values for the 95% confidence interval of square footage for homes?Calculate and report the 95% confidence interval. Show or describe your method of calculation.
Final Conclusions
Summarize your findings: In one paragraph, summarize your findings in clear and concise plain language.
Discuss: Discuss whether you were surprised by the findings. Why or why not?

The B&K Real Estate Company sells homes and is currently serving the Southeast region. It has recently expanded to cover the Northeast states. The B&K realtors are excited to now cover the entire East Coast and are working to prepare their southern agents to expand their reach to the Northeast.
B&K has hired your company to analyze the Northeast home listing prices in order to give information to their agents about the mean listing price at 95% confidence. Your company offers three analysis packages: one based on a sample size of 100 listings, one based on 1,000 listings, and another based on a sample size of 4,000 listings. Because there is an additional cost for data collection, your company charges more for the package with 4,000 listings than for the package with 100 listings.
Bronze Package – Sample size of 100 listings:95% confidence interval for the mean of the Northeast house listing price has a margin of error of $24,500
Cost for service to B&K: $2,000
Silver Package – Sample size of 1,000 listings:95% confidence interval for the mean of the Northeast house listing price has a margin of error of $7,750
Cost for service to B&K: $10,000
Gold Package – Sample size of 4,000 listings:95% confidence interval for the mean of the Northeast house listing price has a margin of error of $3,900
Cost for service to B&K: $25,000
The B&K management team does not understand the tradeoff between confidence level, sample size, and margin of error. B&K would like you to come back with your recommendation of the sample size that would provide the sales agents with the best understanding of northeast home prices at the lowest cost for service to B&K.
In other words, which option is preferable?
Spending more on data collection and having a smaller margin of error
Spending less on data collection and having a larger margin of error
Choosing an option somewhere in the middle
For your initial post:
Formulate a recommendation and write a confidence statement in the context of this scenario. For the purposes of writing your confidence statement, assume the sample mean house listing price is $310,000 for all packages. “I am [#] % confident the true mean . . . [in context].”
Explain the factors that went into your recommendation, including a discussion of the margin of error

The B&K Real Estate Company sells homes and is currently serving the Southeast region. It has recently expanded to cover the Northeast states. The B&K realtors are excited to now cover the entire East Coast and are working to prepare their southern agents to expand their reach to the Northeast.
B&K has hired your company to analyze the Northeast home listing prices in order to give information to their agents about the mean listing price at 95% confidence. Your company offers three analysis packages: one based on a sample size of 100 listings, one based on 1,000 listings, and another based on a sample size of 4,000 listings. Because there is an additional cost for data collection, your company charges more for the package with 4,000 listings than for the package with 100 listings.
Bronze Package – Sample size of 100 listings:95% confidence interval for the mean of the Northeast house listing price has a margin of error of $24,500
Cost for service to B&K: $2,000
Silver Package – Sample size of 1,000 listings:95% confidence interval for the mean of the Northeast house listing price has a margin of error of $7,750
Cost for service to B&K: $10,000
Gold Package – Sample size of 4,000 listings:95% confidence interval for the mean of the Northeast house listing price has a margin of error of $3,900
Cost for service to B&K: $25,000
The B&K management team does not understand the tradeoff between confidence level, sample size, and margin of error. B&K would like you to come back with your recommendation of the sample size that would provide the sales agents with the best understanding of northeast home prices at the lowest cost for service to B&K.
In other words, which option is preferable?
Spending more on data collection and having a smaller margin of error
Spending less on data collection and having a larger margin of error
Choosing an option somewhere in the middle
For your initial post:
Formulate a recommendation and write a confidence statement in the context of this scenario. For the purposes of writing your confidence statement, assume the sample mean house listing price is $310,000 for all packages. “I am [#] % confident the true mean . . . [in context].”
Explain the factors that went into your recommendation, including a discussion of the margin of error

Watch the videos, from Cornell University, about “Effective Study Strategies”:
Effective Study Strategies – Learning Strategies Center (cornell.edu)
Write a brief summary ( at least two paragraph of what you learned after watching this video.