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//Eg-3.9
//pg-88
clear
clc
//cholesky decomposition
A=[1 .5 0;.5 1 .5;0 .5 1];
B=[1;2;3];
[n,n]=size(A);
summ1=0;
summ2=0;
for i=1:n
summ1=0;
for k=1:i-1
summ1=summ1+(L(i,k))^2;
end
L(i,i)=(A(i,i)-summ1)^(1/2);
for j=i+1:n
summ2=0;
for k=1:i-1
summ2=summ2+L(i,k)*L(j,k);
end
L(j,i)=(A(i,j)-summ2)/(L(i,i));
end
end
if L*L'==A then
disp("verification was done")
end
Y=inv(L)*B;
X=inv(L')*Y;
disp(X)
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