The function trid in the book software distribution takes three vectors (n−1) n×1 and (n−1) ×1 and builds a tridiagonal matrix with subdiagonal  diagonal  and superdiagonal  Use trid to construct the...

The function trid in the book software distribution takes three vectors

<sup>(n−1)

n×1</sup>
and

^(n−1)
×1
and builds a tridiagonal matrix with subdiagonal
 diagonal and superdiagonal
 Use trid to construct the
 matrix

 Is A symmetric?

 Is A positive definite?

. Does A have distinct eigenvalues?

 Apply the power method and the inverse power method to estimate the largest and smallest eigenvalues of A.

 Is A ill-conditioned?

 Find the condition number for each eigenvalue of A. Explain the result.