Chapter 2.3, Problem 3CP

Let A be the $n\times n$ matrix with entries $A_{ij}=\left|i-j\right|+1$ . Define $x={\left[1,\mathrm{...},1\right]}^T$ and $b=Ax$ . For

$n=\text{1}00,\text{ 2}00,\text{ 3}00,\text{ 4}00,\text{ and 5}00$, use the MATLAB’s program from Computer Problem 2.1.1 or MATLAB’S backslash command to compute $x_c$, the double precision computed solution. Calculate the infinity norm of the forward error for each solution. Find the five error magnification factors of the problems $Ax=b$, and compare with the corresponding condition numbers.