Question

USING MATLAB/SCILAB: Given the following set of linear equations, solve using LU DECOMPOSITION x1 + 2x2 - x3 + x4 = 5 -x1 - 2x2 - 3x3 + 2x4 = 7 2x1 + x2 - x3 - 5x4 = -1 x1 + x2 + x3 + x4 = 10 Please show me pictures of the matlab/scilab compiler or copy-paste code and output

Answer 1

A = [
1 2 -1 1;
-1 -2 -3 2;
2 1 -1 -5;
1 1 1 1
];
r = [5;7;-1;10];
n = 4;

D=A;d=r;

s=0;
for j=1:n-1
if A(j,j)==0
k=j;
for k=k+1:n
if A(k,j)==0
continue
end
break
end
B=A(j,:); C=r(j);
A(j,:)=A(k,:); r(j)=r(k);
A(k,:)=B; r(k)=C;
end
for i=1+s:n-1
L=A(i+1,j)/A(j,j);
A(i+1,:)=A(i+1,:)-L*A(j,:);
r(i+1)=r(i+1)-L*r(j);
end
s=s+1;
end
%-----------------------------------------------------------------
%Solution of equations
x(n)=r(n)/A(n,n);
for i=n-1:-1:1
sum=0;
for j=i+1:n
sum=sum+A(i,j)*x(j);
end
x(i)=(1/A(i,i))*(r(i)-sum);
end

%------------------------------
%Output
disp('@----------------------------------------------------------@')
disp('Output [A][x]=[b]')
disp('Upper riangular Matrix [B] =');disp(A)
disp('Matrix [b] =');disp(r)
disp('solution of linear equations :');disp(x')

Sample run

Output [A][x]=[b]
Upper riangular Matrix [B] =
   1.00000   2.00000  -1.00000   1.00000
   0.00000  -3.00000   1.00000  -7.00000
   0.00000   0.00000  -4.00000   3.00000
   0.00000   0.00000   0.00000   3.58333
Matrix [b] =
    5.0000
  -11.0000
   12.0000
   13.6667
solution of linear equations :
   11.60465
   -5.27907
   -0.13953
    3.81395