The Frobenius norm of A E Rm*n is defined as i=1 j=1 (a) Write a MATLAB function to compute the Frobenius norm of a given matrix A. Your function header is function x - frobenius (A) mall test where x is the computed value of the Frobenius norm of A. Experiment with a few s matrices to show that your function is correct. (b) Your straightforward implementation of (1) will usually, but not always, give an acceptable result. Here are two potential difficulties: . Even if an element aij is not too large, its square ai, may overflow. If this happens, your function will return "infinity", even though the true Frobenius norm could be well under the machine's overflow threshold. (Recall that a square root is taken at the end of the calculation.) * Even if an element aij is not too small, its square ai may underflow. In MATLAB, an element that underflows is set to 0. Now as long as some of the other elements are large enough, the result still will be acceptable. If, on the other hand, all of the elements under- flow, you r function could incorrectly return 0. Experiment with a few small test matrices to demonstrate these potential difficulties. (c) Write an improved version of the Frobenius norm function that gives an acceptable result even properties discussed above. Describe and justify your when the matrix has one or both of the modifications in the documentation. Compare the efficiency (operation counts) of the two ver- sions of your function