1. Consider the matrix: 3 x 3: [1 2 27 5 678 A = 3 Use the svd() function in MATLAB to compute A₁, the rank-1 approximation of A. Clearly state what A₁ is, rounded to 4 decimal places. Also, compute the root mean square error (RMSE) between A and A₁. 2. Use the svd() function in MATLAB to compute A2, the rank-2 approximation of A. Clearly state what A2 is, rounded to 4 decimal places. Also, compute the root mean square error (RMSE) between A and A2. Which approximation is better, A1 or A₂? Explain. 3. For the 3 x 3 matrix A, the singular value decomposition is A = USV' where U = [u₁ U₂ U3]. Use MATLAB to compute the dot product d₁ = dot (u₁, U₂). Also, use MATLAB to compute the cross product c = cross(u₁, ₂) and dot product d2 = dot(c, u3). Clearly state the values for each of these computations. Do these values make sense? Explain.
1. Consider the matrix: 3 x 3: [1 2 27 5 678 A = 3 Use the svd() function in MATLAB to compute A₁, the rank-1 approximation of A. Clearly state what A₁ is, rounded to 4 decimal places. Also, compute the root mean square error (RMSE) between A and A₁. 2. Use the svd() function in MATLAB to compute A2, the rank-2 approximation of A. Clearly state what A2 is, rounded to 4 decimal places. Also, compute the root mean square error (RMSE) between A and A2. Which approximation is better, A1 or A₂? Explain. 3. For the 3 x 3 matrix A, the singular value decomposition is A = USV' where U = [u₁ U₂ U3]. Use MATLAB to compute the dot product d₁ = dot (u₁, U₂). Also, use MATLAB to compute the cross product c = cross(u₁, ₂) and dot product d2 = dot(c, u3). Clearly state the values for each of these computations. Do these values make sense? Explain.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
Related questions
Question
I need help with this, any help would be greatly appreciated.
![1. Consider the matrix: 3 x 3:
1 22
A = 3 4 5
678
Use the svd() function in MATLAB to compute A1, the rank-1 approximation of A. Clearly state what A₁ is, rounded to 4 decimal places.
Also, compute the root mean square error (RMSE) between A and A₁.
2. Use the svd() function in MATLAB to compute A2, the rank-2 approximation of A. Clearly state what A2 is, rounded to 4 decimal places.
Also, compute the root mean square error (RMSE) between A and 42. Which approximation is better, A1 or A2? Explain.
3. For the 3 x 3 matrix A, the singular value decomposition is A = USV' where U = [u₁ U2 U³]. Use MATLAB to compute the dot product
=
d₁ : dot(u₁, u2). Also, use MATLAB to compute the cross product c = cross(u₁, U₂) and dot product d2 = dot (c, u3). Clearly state the values
for each of these computations. Do these values make sense? Explain.
4. Using the matrix U = [u₁ U2 U3], determine whether or not the columns of U span R³. Explain your approach.
5. Use the MATLAB imshow() function to load and display the image A stored in the provided MATLAB image.mat file (available in the
Supporting Materials area). For the loaded image, derive the value of k that will result in a compression ratio of CR≈ 2. For this value of k,
construct the rank-k approximation of the image.
6. Display the image and compute the root mean square error (RMSE) between the approximation and the original image. Make sure to
include a copy of the approximate image in your report.
7. Repeat steps 5 and 6 for CR ~ 10, CR ~ 25, and CR 75. Explain what trends you observe in the image approximation as CR increases and
provide your recommendation for the best CR based on your observations. Make sure to include a copy of the approximate images in your
report.
Type here to search
EPIC
GAMES
O
031
く
2
5:12 PM
8/10/2022](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc02858c3-02a4-4a72-a738-466a3d85bed1%2F6c722866-61e7-44dd-a490-1a8d3ca46fa5%2Fx3udck_processed.png&w=3840&q=75)
Transcribed Image Text:1. Consider the matrix: 3 x 3:
1 22
A = 3 4 5
678
Use the svd() function in MATLAB to compute A1, the rank-1 approximation of A. Clearly state what A₁ is, rounded to 4 decimal places.
Also, compute the root mean square error (RMSE) between A and A₁.
2. Use the svd() function in MATLAB to compute A2, the rank-2 approximation of A. Clearly state what A2 is, rounded to 4 decimal places.
Also, compute the root mean square error (RMSE) between A and 42. Which approximation is better, A1 or A2? Explain.
3. For the 3 x 3 matrix A, the singular value decomposition is A = USV' where U = [u₁ U2 U³]. Use MATLAB to compute the dot product
=
d₁ : dot(u₁, u2). Also, use MATLAB to compute the cross product c = cross(u₁, U₂) and dot product d2 = dot (c, u3). Clearly state the values
for each of these computations. Do these values make sense? Explain.
4. Using the matrix U = [u₁ U2 U3], determine whether or not the columns of U span R³. Explain your approach.
5. Use the MATLAB imshow() function to load and display the image A stored in the provided MATLAB image.mat file (available in the
Supporting Materials area). For the loaded image, derive the value of k that will result in a compression ratio of CR≈ 2. For this value of k,
construct the rank-k approximation of the image.
6. Display the image and compute the root mean square error (RMSE) between the approximation and the original image. Make sure to
include a copy of the approximate image in your report.
7. Repeat steps 5 and 6 for CR ~ 10, CR ~ 25, and CR 75. Explain what trends you observe in the image approximation as CR increases and
provide your recommendation for the best CR based on your observations. Make sure to include a copy of the approximate images in your
report.
Type here to search
EPIC
GAMES
O
031
く
2
5:12 PM
8/10/2022
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 4 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.Recommended textbooks for you
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
C How to Program (8th Edition)
Computer Science
ISBN:
9780133976892
Author:
Paul J. Deitel, Harvey Deitel
Publisher:
PEARSON
Database Systems: Design, Implementation, & Manag…
Computer Science
ISBN:
9781337627900
Author:
Carlos Coronel, Steven Morris
Publisher:
Cengage Learning
Programmable Logic Controllers
Computer Science
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education