In this experiment note that the questions call for the creation of a function M

Question

In this experiment note that the questions call for the creation of a function M-file to solve the problem. As before your function M-files will have to include help files, version information, error detection and extensive comments. You will also have to avoid bad practice such as choosing meaningless names for variables and/or functions and embedding universal numbers into the code. The module notes discuss the algorithms, sic Newton-Raphson algorithm, Gaussian elimination (with total pivoting) and Gauss-Seidel which you are called upon to employ, but they do not fully indicate how to implement these algorithms as MATLAB function M-files.

Problem 2 Create a MATLAB function M-file to solve an arbitrary system of linear equations by Gaussian elimination with total pivoting. Apply the resulting M-file to solve the system of linear equations (2). Is it possible to solve this system using Gaussian elimination without pivoting? Check your results by re-solving the equations using built-in MATLAB commands. The section on matrices in experiment MS01 offered two ways for you to solve a system of linear equations using built-in MATLAB commands.

Explanation / Answer

MATLAB CODE:

clc;

clear all;

close all;

%Let below matrix represents system of linear equations

a =[0 3.2 0 1 -0.5 0; -2.1 2.2 7.5 -1.9 1 -2.5; 9.6 3 0 1.2 5.5 -7.5; 2 1 -5.7 -11 -1 6.1; 3 0 -3 -4 10 2.6];

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Gauss elimination method [m,n)=size(a);

[m,n]=size(a);

for j=1:m-1

for z=2:m

if a(j,j)==0

t=a(j,:);a(j,:)=a(z,:);

a(z,:)=t;

end

end

for i=j+1:m

a(i,:)=a(i,:)-a(j,:)*(a(i,j)/a(j,j));

end

end

x=zeros(1,m);

for s=m:-1:1

c=0;

for k=2:m

c=c+a(s,k)*x(k);

end

x(s)=(a(s,n)-c)/a(s,s);

end

x'

OUTPUT:

ans =
-0.8769
0.1328
-0.7266
-0.3407
0.1688
>>

Verification:

A=[0 3.2 0 1 -0.5; -2.1 2.2 7.5 -1.9 1; 9.6 3 0 1.2 5.5; 2 1 -5.7 -11 -1 ; 3 0 -3 -4 10];

B=[0;-2.5;-7.5;6.1;2.6];

x=inv(A)*B
x =
-0.8769
0.1328
-0.7266
-0.3407
0.1688
>>

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