MATLAB IS NEEDED FOR THIS PROBLEM.

= Problem 3 [3 pts]: Let A [aij] be an n x n matrix with entries (n+1- max(i,j), isj +1 aij 10, i>j +1 where max(i,j) returns the larger one of i and j (e.g., max(1,2) = 2 , max(3,2) = 3). This is an example of an upper Hessenberg matrix. (1) Analytically compute || A||00 and ||A||1 for n = 10. (2) Write a program to construct matrix A for any n. Output A for n = 10. (3) For n = 10, use your program to calculate ||A||1, ||A||2, || A||co, and ||A|le (the Frobenius norm). Verify the following inequalities ||A||2 j +1 where max(i,j) returns the larger one of i and j (e.g., max(1,2) = 2 , max(3,2) = 3). This is an example of an upper Hessenberg matrix. (1) Analytically compute || A||00 and ||A||1 for n = 10. (2) Write a program to construct matrix A for any n. Output A for n = 10. (3) For n = 10, use your program to calculate ||A||1, ||A||2, || A||co, and ||A|le (the Frobenius norm). Verify the following inequalities ||A||2