This is a matlab question. If possible please include code as well as answers. Thank you!

The following is an example of a matrix that is tridiagonal: T =[2 3 0 0 0; 3 2 3 0 0; 0 3 2 3 0; 0 0 3 2 3; 0 0 0 3 2] Write a function T = tridiag(n,d,c) which produces an n n tridiagonal matrix T which has the value d along its main diagonal, the value c along the diagonals above and below the main diagonal, and zeros elsewhere. Test your function with n = 10, d = 6 and c = 1. If your code works, find sum(sum(T^3)), and turn in the answer. Matlab has a built-in function that will do this, but the point of the problem is to practice using loop. So use loops.

The sequence xn+1 = rxn (1 xn) is called the logistic map. If 1 < r < 3, the sequence will converge to the number r1 r . For example, if we let r = 2.5 and x0 = 0.5, the first 16 terms of the sequence are:

x = 0.5000

0.6250

0.5859

0.6065

0.5966

0.6017

0.5992

0.6004

0.5998

0.6001

0.5999

0.6000

0.6000

0.6000

0.6000

0.6000

Now, for 3 < r < 3.4, the sequence will not converge but rather will oscillate between two values. Let x0 = 0.5 and r = 3.1. What two values does the sequence oscillate between?