1) Let eij be the per-pixel error, i.e. the difference between the original image and the compressed version at coordinates row and column . Explain why this expression gives the upper bound on the per-pixel error: where is the rank of the original matrix (i.e., the total number of singular values), is the th singular value, is defined above, and is a constant that you must fill in (in other words, is just a simple constant number, which you can arrive at through understanding what is being added up by the formula, and how it relates to the worst-case error). For full credit, you must determine and explain how the formula is calculating worst-case error. 2) Explain how you could use the formula in (d) to choose the smallest possible value of such that the per-pixel error at any pixel is guaranteed to be no greater than , for some small tolerance > 0.