The Hilbert matrices have elements ij and are notoriously ill-conditioned. Create A = hilb(8). Perturb A(1,8) by 10−5, and call the perturbed matrix Let Compute and follow by computing and . Is...

The

Hilbert matrices have elements

_ij

and are notoriously ill-conditioned.

Create A = hilb(8). Perturb A(1,8) by 10−5, and call the perturbed matrix

Let

Compute

and follow by computing

and
. Is ill-conditioning evident

Compute the condition number of hilb(8) using the MATLAB command cond(A) and then use it to compute the theoretical upper bound given in Theorem 10.4, part

Do your calculations verify the inequality