The following MATLAB commands generate the matrix $B,$ the matrix $A=B^{T}B$ and two vectors $b$ and $z($these commands have already been entered for you$)$

$n=70$;

$B=$eye$(n)-$triu$(ones(n),1)$;

$A=B^{\text{'}**B}$;

$Z=$ones$(n,1)$;

$b=A^{**}z$

Similarly to the previous problem, the exact solution of the system $Ax=b$ is the vector $z$ Compute the solution using the al ${?}^{?}$ and using the inverse:

$x=$Alb

$y=$inv$(A{)}^{**}b$;

Compare the accuracy of the two methods as in the previous problem, that is$,$ compute

${\displaystyle \underset{?}{\overset{?}{}}}(\frac{?}{abs}(x-z))$

${\displaystyle \underset{?}{\overset{?}{}}}(\frac{?}{abs}(y-z))$

Store the results in the variables err$1$ and err$2$ respectively.

Recall that the two commands above compute how close the computed solution is to the exact solution. Thus the naller value is associated to the more accurate method.

Don't worry about MATLAB warning messages. They are due to the fact that the matrix B is $($numerically$)$ close to singular.

Which method produces the more accurate solution? You will be asked to answer this question in the next exercise.

Don't forget to include your name as a comment in your script.