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//Example 3.10
//Triangularization Method
//Page no. 62
clc;clear;close;
A=[2,4,-6;1,5,3;1,3,2];
B=[-4;10;5];
printf('A can be factorizaed as follows:\n')
printf('\tL\t\t *\t\tU\t\t =\t\tA')
U(2,1)=0;U(3,1)=0;U(3,2)=0;
L(1,2)=0;L(1,3)=0;L(2,3)=0;
for i=1:3
L(i,i)=1
end
for i=1:3
U(1,i)=A(1,i)
end
L(2,1)=1/U(1,1);
for i=2:3
U(2,i)=A(2,i)-U(1,i)*L(2,1);
end
L(3,1)=1/U(1,1);
L(3,2)=(A(3,2)-U(1,2)*L(3,1))/U(2,2);
U(3,3)=A(3,3)-U(1,3)*L(3,1)-U(2,3)*L(3,2);
printf('\n')
for i=1:3
for j=1:3
printf('%.2f\t',L(i,j))
end
if(i==2)
printf(' * ')
else
printf('\t')
end
for j=1:3
printf('%.2f\t',U(i,j))
end
if(i==2)
printf(' = ')
else
printf('\t')
end
for j=1:3
printf('%.2f\t',A(i,j))
end
printf('\n')
end
printf('\nY=U*X')
Y=inv(L)*B
X=inv(U)*Y
printf('\n\nX=')
for i=1:3
printf('\n %i',X(i,1))
end
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