This problem is motivated by a discussion in the classic book by Wilkinson Consider the class of matrices a. If you have not done Problem 18.30, write a MATLAB function, wilkcondeig, that builds Bn. ...

This problem is motivated by a discussion in the classic book by Wilkinson

Consider the class of matrices

a. If you have not done Problem 18.30, write a MATLAB function, wilkcondeig, that builds Bn.

Using MATLAB, let

and show that the largest eigenvalues of

₂₀
are well-conditioned, while the smallest ones are quite ill-conditioned.

Show that the determinant of

_n
is one for all

If we assign

_n

the determinate becomes

Let


^-10

and compute the determinant.

Prove that the determinant of a matrix is equal to the product of its eigenvalues.

Explain why there must be large eigenvalues in the perturbed

_n