rate 100% Programming Part: For each programming problem, please submit the code

Question

rate 100%

Programming Part: For each programming problem, please submit the code and the output by pasting them into a word document and attaching them to your homework. 1. Implement the back-substitution algorithm in Matlab to solve Ux b where i j i > j cos(ij), U=[uij]10x10, and b = [balioxi, bil = tan(i) thi = 2. Gauss-Jordan Method: This method is used to solve linear systems as an alternative to Gaussian Elimination. In addition to using pivot element akto eliminate every element below in the kth column, but also use it to eliminate every element above it. This results in the augmented matrix being diagonal and therefore back-substitution is not needed (instead xk =-for k = 1, m) (k-1) b(n-1) 0...0bn-1) (n-1) (n-1) Modify the Gaussian Elimination code to incorporate the Gauss-Jordan Method and re-solve problem 2 (above) to check your work.

Explanation / Answer

Program:

% function []=backsubstitution()

clc,clear

% This function solves system of linear equations Ux=b

% where U is upper trianglular matrix and b is constant matrix

%input U and b

% output x

%set Upeer Triangular Matrix

for i=1:10

    b(i,1)=tan(i);

    for j=1:10

        if i>j

            U(i,j)=0;

        else

            U(i,j)=cos(i*j);

        end

    end

end

x=zeros(10,1);

for i=10:-1:1

        x(i)=b(i)/U(i,i);

        b(1:i-1)=b(1:i-1)-(U(1:i-1,i)*x(i));

end

Output:

-748.919602967446

-398.474754316029

-207.229883076974

-83.9978506857593

42.8937571027075

-75.7438881957954

51.4967723407501

-17.5075235418190

-0.148602916312626

0.751880595792855

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