In this problem we are going to use a multiply a vector by different sizes of hilbert matricies and check the uncertainty in this multiplication.

Multiply a $5\text{'}$s vector by a series of hilbert matricies ranging from the $11$ Hilbert matrix to the $3030$ Hilbert matrix. You can use the hilb

function to generate these matricies. Since these matricies are different sizes you will also have to adjust your $5\text{'}$s vector for each

multiplication. Next attempt to regenerate the original vector using the $\frac{\frac{?}{?}}{?}$ operator. The first iteration of this might look something like:

$x=5^{**}$ ones $(1,1)$

$A=$ hilb$(1)$

$B=A^{**}x$

$x_{n}ew=$ AIB

For each iteration calculate the uncertainty in this matrix using the formula: $lon=\frac{||xnew-x||}{||x||}**100,$ use the $2-$norm. Generate a semilogy plot

of $1$:$30$ vs uncertainty.Use Matlab code