Question

2 Write an M-file to generate E (1/(n+1)Cjwhere, C-1) ifi-j i,j-1 fj >1 Having generated E. for n-20 solve E*x-b where b = [ 1:n11 by Gaussian-Elimination Method

Can you make matlab solve it?

Answer 1

Ans)

%======================MATLAB CODE=============

%Generation of Matrix "E"

n=20;

for i=1:20

for j=1:20

if i==j

C(i,j)=i*(n-i+1);

E(i,j)=(1/(n+1))*C(i,j);

elseif j>i

C(i,j)=C(i,j-1)-i;

E(i,j)=(1/(n+1))*C(i,j);

else

C(i,j)=C(j,i);

E(i,j)=(1/(n+1))*C(i,j);

end

end

end

b=[1:n]'; %MATRIX "b"

a=[E b]; %Coefficient Matrix used for Gauss Elimination below

%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

disp('Gauss elimination method:');

x' %solution vector

===============================================

The solution when you run above code is

2 ans 1.1657e-16 2.3373e-16 4.6876e-16 9.4042e-16 1.1796e-15 1.6579e-15 3.0928e-15 3.8260e-15 2.8866e-15 3.3912e-15 2.9310e-15 2.4672e-15 -4.9960e-15 1.5226e-15 5.6991e-15 3.1974e-15 6.6613e-15 2.3685e-15 2.6645e-15 2.1000e+01