[ANSWER] MAT 350 Project Two Guidelines and Rubric / MAT 350 Project Two Template

MAT 350 Project Two Guidelines and Rubric

MAT 350 Project Two Template

MAT 350: Applied Linear Algebra

Problem 1

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

Solution

A1 = 3×3

ans = 1

RMSE = 0.8155

Problem 2

Use the svd() function in MATLAB to compute , the rank-2 approximation of A. Clearly state what  is, rounded to 4 decimal places. Also, compute the root-mean square error (RMSE) between A and . Which approximation is better,  or ? Explain.

Solution:

A2 = 3×3

1.0100    1.8213    2.1469

2.9907    4.1656    4.8639

6.0029    6.9476    8.0431

ans = 2

RSME2 = 0.2689

Explain:

Problem 3

For the  matrix A, the singular value decomposition is where. Use MATLAB to compute the dot product. Also, use MATLAB to compute the cross product  and dot product. Clearly state the values for each of these computations. Do these values make sense? Explain.

Solution:

U1 = 3×1

-0.2055

-0.4900

-0.8471

U2 = 3×1

-0.6658

-0.5644

0.4880

U3 = 3×1

-0.7172

0.6643

-0.2103

d1 = -6.9000e-06

c = 3×1

-0.7172

0.6643

-0.2103

d2 = 0.9999

Explain:

Problem 4

Using the matrix , determine whether or not the columns of U span . Explain your approach.

Solution:

U = 3×3

ans = 3

Explain:

Problem 5

Use the MATLAB imshow() function to load and display the image A stored in the image.mat file, available in the Project Two Supported Materials area in Brightspace. For the loaded image, derive the value of k that will result in a compression ratio of . For this value of k, construct the rank-k approximation of the image.

Solution:

CR = 2.0000

A801 = 2583×4220

ans = 801

A801