Please solve using Numerical Methods for Engineers and Scien

Please solve using Numerical Methods for Engineers and Scientists Using MATLAB® by Ramin S. Esfandiari

72. A Write a user-defined function with function call Cok,k,Mnorm Gen Iter 2 b,x0,tol,kmax) to solve b using the general iterative method as follows: The coefficient matrix must be split as A E Q P, where Q has the same diagonal, upper diagonal (one level higher than the diagonal), and lower diagonal one level lower than the diagonal) entries as A with all other entries zero. The input/out put arguments, as well as the terminating condition are as in functions Jacobi and Gaussseidel (Section 4.5) with the same default values. The output Mnorm is the infinite norm of the corresponding iteration matrix. Apply Genlter 2 to the linear system -8 0 1 -1 3 0 6 0 1 4 16 (0) 1 x 3 1 -7 10 11

Solution

[7352][xy]=[322][7532][xy]=[322]

coefficientvariableconstantmatrixmatrixmatrixcoefficientvariableconstantmatrixmatrixmatrix

First, find the inverse of the coefficient matrix. The inverse of [7352][7532] is

17(2)(3)(5)[2357]=129[2357]=[229329529729]17(2)(3)(5)[2537]=129[2537]=[229529329729]

Next, multiply each side of the matrix equation by the inverse matrix. Since matrix multiplication is not commutative, the inverse matrix should be at the left on each side of the matrix equation.

[229329529729][7352][xy]=[229329529729][322][229529329729][7532][xy]=[229529329729][322]

[1001][xy]=[45][1001][xy]=[45]

The identity matrix on the left verifies that the inverse matrix was calculated correctly.

[xy]=[45][xy]=[45]

The solution is (4,5)