1. If a symmetric tridiagonal matrix is unreduced no zeros on the subdiagonal and thus none on the superdiagonal  it must have distinct real eigenvalues Problem When testing for ghost eigenvalues, why...

1.

If a symmetric tridiagonal matrix is unreduced
no zeros on the subdiagonal and thus none on the superdiagonal it must have distinct real eigenvalues
Problem
When testing for ghost eigenvalues, why is knowing this result important

2.

Using the function biharmonic_op in the software distribution, build a block pentadiagonal matrix of size
Use eigs to compute the six largest eigenvalues in magnitude, and then apply the power method in an attempt to compute the largest eigenvalue. Explain why you have great difficulty or fail to compute an accurate result.