Starting with a vector of three 1s use power iteration to

Question

For the matrix of Exercise 11.1.4:

(a) Starting with a vector of three 1's, use power iteration to find an approximate value of the principal eigenvector.

(b) Compute an estimate the principal eigenvalue for the matrix.

(c) Construct a new matrix by subtracting out the effect of the principal eigenpair, as in Section 11.1.3. (d) From your matrix of

(c), find the second eigenpair for the original matrix of Exercise 11.1.4.

(e) Repeat (c) and (d) to find the third eigenpair for the original matrix.

Exercise 11.1.4

Find the eigenpairs for the following matrix:

using the method of Section 11.1.2.