Consider the system 1 12 13 14 15 12 13 14 15 16 13 14 15 16

Consider the system [1 1/2 1/3 1/4 1/5 1/2 1/3 1/4 1/5 1/6 1/3 1/4 1/5 1/6 1/7 1/4 1/5 1/6 1/7 1/8 1/5 1/6 1/7 1/8 1/9] x = [1 1 1 1 1] Show that x = [5 -120 630 -1120 630]^T is the unique solution to the above system of equations. Use Matlab to approximate the solution to the system of equations. What is the relative error in each entry of the result?

Solution

clc
clear all
A= [1 1/2 1/3 1/4 1/5;
1/2 1/3 1/4 1/5 1/6;
1/3 1/4 1/5 1/6 1/7;
1/4 1/5 1/6 1/7 1/8;
1/5 1/6 1/7 1/8 1/9];
B=[1;1;1;1;1];
AB(1:5,1:5)=A;
AB(1:5,6)=B;
rAB=sprank(AB)
rA=sprank(A)
if(rAB==rA)
disp(\'rank(AB)=rank(A). So system has unique solution\');
x=inv(A)*B
end
%relative error in each entry of result
x1=([5 -120 630 -1120 630])\';
error=(x-x1)./(x1)