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9.3. (a) Write a MATLAB program that sets up a 15 x 40 matrix with entries 0 everywhere except for the values 1 in the positions indicated in the picture below. The upper-leftmost 1 is in position (2,2), and the lower-rightmost 1 is in position (13, 39). This picture was produced with the command spy (A). HELLO 10- 15. 5 10 15 20 25 30 35 40 (b) Call svd to compute the singular values of A, and print the results. Plot these numbers using both plot and semilogy. What is the mathematically exact rank of A? How does this show up in the computed singular values? (c) For each i from 1 to rank(A), construct the rank-i matrix B that is the best approximation to A in the 2-norm. Use the command pcolor (B) with colormap(gray) to create images of these various approximations.

9.3. (a) Write a MATLAB program that sets up a 15 x 40 matrix with entries 0 everywhere except for the values 1 in the positions indicated in the picture below. The upper-leftmost 1 is in position (2,2), and the lower-rightmost 1 is in position (13, 39). This picture was produced with the command spy (A). HELLO 10- 15. 5 10 15 20 25 30 35 40 (b) Call svd to compute the singular values of A, and print the results. Plot these numbers using both plot and semilogy. What is the mathematically exact rank of A? How does this show up in the computed singular values? (c) For each i from 1 to rank(A), construct the rank-i matrix B that is the best approximation to A in the 2-norm. Use the command pcolor (B) with colormap(gray) to create images of these various approximations.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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9.3. (a) Write a MATLAB program that sets up a 15 x 40 matrix with entries 0 everywhere except for the values 1 in the positions indicated in the picture below. The upper-leftmost 1 is in position (2,2), and the lower-rightmost 1 is in position (13, 39). This picture was produced with the command spy (A). HELLO 5- 10- 15-. 5 10 15 20 25 30 35 40 (b) Call svd to compute the singular values of A, and print the results. Plot these numbers using both plot and semilogy. What is the mathematically exact rank of A? How does this show up in the computed singular values? (c) For each i from 1 to rank(A), construct the rank-i matrix B that is the best approximation to A in the 2-norm. Use the command pcolor (B) with colormap(gray) to create images of these various approximations.
Transcribed Image Text:9.3. (a) Write a MATLAB program that sets up a 15 x 40 matrix with entries 0 everywhere except for the values 1 in the positions indicated in the picture below. The upper-leftmost 1 is in position (2,2), and the lower-rightmost 1 is in position (13, 39). This picture was produced with the command spy (A). HELLO 5- 10- 15-. 5 10 15 20 25 30 35 40 (b) Call svd to compute the singular values of A, and print the results. Plot these numbers using both plot and semilogy. What is the mathematically exact rank of A? How does this show up in the computed singular values? (c) For each i from 1 to rank(A), construct the rank-i matrix B that is the best approximation to A in the 2-norm. Use the command pcolor (B) with colormap(gray) to create images of these various approximations.
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