CHOOSE 1 ONLY! We are coding in Python and can use Scipy and Numpy. Do not have to do both, just 4a or 4b, your choice!

Choose Only One b 4a Consider forming the matrix vector product Ax, where both A and x possess rounding errors, namely that A and be may admit perturbations 6A and s.t. and where l I denotes the entrywise absolute value of a matrix/vector. Give a bound for the relative error in Ar. You may pick the error metric(norm). Assume all arithmetic is otherwise exact. 4.b. Write code, using the scipy LU-factorization functions, to compute the partial-pivoting LU factorization of random, normally (standard) distributed matrices(use numpy.random.randn) of size 24,25,... 20. Produce statistics(use at least 1000 samples) of the average relative error of PA - LU. Again, you may pick any reasonable error metric. Choose Only One b 4a Consider forming the matrix vector product Ax, where both A and x possess rounding errors, namely that A and be may admit perturbations 6A and s.t. and where l I denotes the entrywise absolute value of a matrix/vector. Give a bound for the relative error in Ar. You may pick the error metric(norm). Assume all arithmetic is otherwise exact. 4.b. Write code, using the scipy LU-factorization functions, to compute the partial-pivoting LU factorization of random, normally (standard) distributed matrices(use numpy.random.randn) of size 24,25,... 20. Produce statistics(use at least 1000 samples) of the average relative error of PA - LU. Again, you may pick any reasonable error metric