Consider the symmetric matrix                                                 (a) What are the eigenvalues for this matrix? Explain why this matrix does not have a dominant eigenvalue. (b) Suppose the...

Consider the symmetric matrix

(a) What are the eigenvalues for this matrix? Explain why this matrix does not have a dominant eigenvalue.

(b) Suppose the power method is applied to
A. What does (4.13) reduce to? Explain why the method does not converge.

(c) Let
B
=
A−μ
I. Explain why the power method, when applied to
B, will converge for any nonzero value for. Also, explain how to pick values for
 to compute the two eigenvalues for
A
using the power method for each.