$($a$)$ The exact solution of the system $Ax=b$ should be

the vector $z.$ Why? Explain. One could compute the

solution in MATLAB using the $"\frac{\frac{?}{?}}{?}"$ operation or by

computing $A^{-1}$ and then multiplying $A^{-1}$ times $b.$

for both speed and accuracy. One can use MAT

LAB's tic and toc commands to measure the

elapsed time for each computation. To do this, use

the commands

tic, $x=\frac{A}{\frac{?}{?}}b$; toc

tic, $y=$inv$(A)**b$; toc

Which method is faster?

To compare the accuracy of the two methods,

we can measure how close the computed solutions

$x$ and $y$ are to the exact solution $z.$ Do this with the

commands

max$(\frac{?}{abs}(x-z))$

max$(\frac{?}{abs}(y-z))$

Which method produces the most accurate solution?

$($b$)$ Repeat part $($a$),$ using $n=500$ and $n=1000.$ I want both Matlab process and also answer each questions.