1. Load the image dog.jpg and compute the economy SVD. 2. Compute the relative reconstruction error of the truncated SVD in the Frobenius norm as a function of the rank r. Hint: The python command for frobenius norm of a matrix is scipy.linalg.norm (). In Matlab, use norm (X, 'fro'). 3. Square this error to compute the fraction of missing variance as a function of r. 4. Plot the quantities computed in (b) and (c) along with the cumulative sum of singular values as a function of r. 5. Find the rank r where the reconstruction captures 99% of the total variance. Compare this with the rank r where the reconstruction captures 99% in the Frobenius norm and with the rank r that captures 99% of the cumulative sum of singular values.