Part A)
Program code:
Main function:
Am=[ 10 -7 0; 0 2.5 5; 0 0 6.2]
Bm=[7;2.5;6.2];
LUEstimate(Am,Bm)
Supporting function:
function[L,U,X]=LUEstimate(Am,Bm)
[a b]=size(Am);
if (a ~= b )
disp ( 'Error' );
return;
end;
% Seperate A matrix into L and U
L=zeros(a,a);
U=zeros(a,a);
for i=1:a
% Find L
for k=1:i-1
L(i,k)=Am(i,k);
for j=1:k-1
L(i,k)= L(i,k)-L(i,j)*U(j,k);
end
L(i,k) = L(i,k)/U(k,k);
end
% Find U
for k=i:a
U(i,k) = Am(i,k);
for j=1:i-1
U(i,k)= U(i,k)-L(i,j)*U(j,k);
end
end
end
for i=1:a
L(i,i)=1;
end
% Display L and U
U
L
b=zeros(a,1); % initiation for B
B(1)=Bm(1)/L(1,1);
for i=2:a
%B(i)=Bm(i)-L(i,1)*B(1)-L(i,2)*B(2)-L(i,3)*B(3);
B(i)=-L(i,1)*B(1);
for k=2:i-1
B(i)=B(i)-L(i,k)*B(k);
end;
B(i)=(Bm(i)+B(i))/L(i,i);
end;
B
x=zeros(a,1);
x(a)=B(a)/U(a,a);
i=a-1;
q=0;
while (i~= 0)
x(i)=-U(i,a)*x(a);
q=i+1;
while (q~=a)
x(i)=x(i)-U(i,q)*x(q);
q=q+1;
end;
x(i)=(B(i)+x(i))/U(i,i);
i=i-1;
end;
Linear equation question Use Matlab for b) and c) and show all the work Oct 3,ao16...