Suppose the solution x ER", of Ax = b with A E Rnxn being nonsingular and upper triangular, is known. = 1. Present mathematically an algorithm for the computation of y in Ay 7, where e Rn differs from b e Ronly in its ith element. Implement your algorithm in a MATLAB function and run it on a random example. An n = 7 example would suffice. Much attention should be paid on the efficiency of your algorithm and its implementation. 2. Explain, in terms of flops, why knowing x makes the computation of y more efficient in general. Suppose the solution x ER", of Ax = b with A E Rnxn being nonsingular and upper triangular, is known. = 1. Present mathematically an algorithm for the computation of y in Ay 7, where e Rn differs from b e Ronly in its ith element. Implement your algorithm in a MATLAB function and run it on a random example. An n = 7 example would suffice. Much attention should be paid on the efficiency of your algorithm and its implementation. 2. Explain, in terms of flops, why knowing x makes the computation of y more efficient in general