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Please help me figure out these questions with valid code and explaining what is happening. Its a cross over from computer science and applied linear algebra. Im stumped.

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Problem 1 Use the svd() function in MATLAB to compute A, , the rank-1 approximation of A. Clearly state what A, is, rounded to 4 decimal places. Also, compute the root-mean square error (RMSE) between A and Al. Solution: Problem 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, A, or A2? Explain. Solution: Explain: Problem 3 For the 3 x 3 matrix A, the singular value decomposition is A = USV' where U = [ul u; u3]. Use MATLAB to compute the dot product dl = dorm], 111). Also, use MATLAB to compute the cross product c = cross(u,, u;) and dot product 11; = dot(c,u3). Clearly state the values for each of these computations. Do these values make sense? Explain. Solution: Explain: Problem 4 Using the matrix U = [u] u; "3], determine whether or not the columns of U span R3. Explain your approach. Solution: Explain:

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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 CR z 2. For this value of k, construct the rank-k approximation of the image. Solution: Explain: Problem 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. Solution: Problem 7 Repeat Problems 5 and 6 for CR : 10, CR : 25, and CR m 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. Solution: Explain:

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