Problem 6. (i) suppose that a rank-k approximation, for some k, gives an acceptable approximation. how much data is needed to represent the rank-k approximation? your answer should be an expression in terms of k, m and n. hint: you need k columns of u, k columns of v , and k singular values of s. (ii) the ratio of the amount of data used for the approximation (which you found in part (i)) and the amount of data of the (original format of the) picture is the compression rate. find the compression rate for the value of the rank you determined in problem 4. what does the compression rate represent? hint: after finding the compression rate for the value of the rank you determined in problem 4, you may want to present this number as a percentage.