2. Consider the class of n n matrices An whose entries are defined by the formula ai,-V 2 n/ 10. (a) Create a short MATLAB function which takes n as its input and outputs the corresponding n xn matrix A (b) Use MATLAB's \ command to solve the system Ant-b, where b = [2, 2, , 2,2]T has the appropriate number of entries. From the perspective of ill-conditioning, how many digits of the approximate solution can we trust? Provide justification/evidence to support your answer. You may find MATLAB's cond function useful here. (c) Similar to part (b), solve the systern A200x = b where b = A200 * [1,1, , 1, 1]T, what is the actual solution to this system (hint: don't overthink this one)? Calculate the relative forward and backward errors for your approximate solution. Now compute the error magnification factor and compare it to the condition number of A200 (d) Suppose that I require a more accurate solution of the system in part (c) than double-precision allows. If I were freely able to tweak the number of bits that MATLAB can store in the mantissa for any given floating point number, roughly how many bits would there have to be in order for us to obtain an answer accurate to 20 (decimal) digits