Use mathematical induction to prove the following: An = (1 3n − 1 0 3n) for all integers n ≥ 1, where A = (1 2 0 3) After you have proved the above statement using mathematical induction, write a MATLAB program to verify that the formula holds for n = 1, 2, . . . , num, where num is entered by the user. That is, for each n = 1, 2, . . . , num, get MATLAB to compute A n and then check that the result is equal to (1 3n − 1 0 3n) Run the program with num = 10.