A Toeplitz matrix is an m times n matrix in which each descending diagonal from left to right is constant. For example A = [4 3 2 1 5 4 3 2 6 5 4 3] is a 3 by 4 Toeplitz matrix. The entries of the matrix A come from a vector a that has m + n-1 entries. In the example above, a = [1; 2; 3; 4; 5; 6]. In this exercise, you will write a code that will create a Toeplitz matrix. Then you will run the function for the given m, n, and a to get the corresponding Toeplitz matrices. **Write a MATLAB function A = toeplitz (m, n, a) which produces an m times n Toeplitz matrix using the entries of an (m + n-1) times 1 vector a, by assigning A(i, j) = a(n+i-j) i = 1: m, j = 1: n **Type the function toeplitz in your diary file. **Run the function A= toeplitz (m, n, a) on the following sets of variables. Display vector a for each of the below. (a) m=4; n=3; a=transpose([1:61) (b) m=3; n=4; a=randi(10, 6, 1) (c) m=4, n=4; a=[zeros(3, 1); [1:4]'] **Construct a vector a that will define a 5 by 5 Toeplitz upper triangular matrix with random integer entries that range between 10 and 100. Display the vector a **Run the function A = toeplitz (m, n, a) for the variables indicated above. **Output a 4 by 4 identity matrix by running the function A= toeplitz (m, n, a) on the corresponding set of variables. Display the vector a