Computer Science ---Numerical Computation for Algebraic Problems---linear system

3. Write a MatlAB function that solves pentadiagonal systems of equations of size n. A pentadiagonal matrix is a banded one with bandwidth - 5 and p q 3. Assume that no pivoting is needed, but do not assume that the matrix A is symmetric. Your program should expect as input six vectors of size n, n - 1 or n - 2: one right hand side b and the five nonzero diagonals of A It should calculate and return x-A-'b using a Gaussian elimination variant that requires O(n) flops and consumes no additional space as a function of n (i.e., in total 7n storage locations are required) Try your program on the matrix defined by n 100.000, ai,2-ai+24 2, ai,i+1-ai+1,i = _i, and ai,i 82, for all i such that the relevant subscripts fall in the range 1 to n. Derive a right hand side vector b Axexact using Xeract (1, 1,..., 1,1)T. Then solve for x given this b and record |leract xl 2. 3. Write a MatlAB function that solves pentadiagonal systems of equations of size n. A pentadiagonal matrix is a banded one with bandwidth - 5 and p q 3. Assume that no pivoting is needed, but do not assume that the matrix A is symmetric. Your program should expect as input six vectors of size n, n - 1 or n - 2: one right hand side b and the five nonzero diagonals of A It should calculate and return x-A-'b using a Gaussian elimination variant that requires O(n) flops and consumes no additional space as a function of n (i.e., in total 7n storage locations are required) Try your program on the matrix defined by n 100.000, ai,2-ai+24 2, ai,i+1-ai+1,i = _i, and ai,i 82, for all i such that the relevant subscripts fall in the range 1 to n. Derive a right hand side vector b Axexact using Xeract (1, 1,..., 1,1)T. Then solve for x given this b and record |leract xl 2