One estimate that can be used for the condition number of a matrix is the ratio of the largest and smallest eigenvalues. In fact, for real symmetric matrices, that turns out to be exactly the condition number. Consider the matrix A =

2 1 0

1 2 1

0 1 2

(a) Perform 3 iterations of the Power method to estimate the largest eigenvalue.

(b) Perform 3 iterations of the Inverse Power method to estimate the smallest eigenvalue. Make sure to do an LU factorization and use LU for each iteration.

(c) Compute the ratio of your estimates of the largest and smallest eigenvalues.

(d) Compare with MATLABs values for cond and the values from eig