Assume that the largest eigenvalue λ1 in magnitude and an associated eigenvector v(1) have been obtained for the n × n symmetric matrix A. Show that the matrix
has the same eigenvalues λ2, . . . , λn as A, except that B has eigenvalue 0 with eigenvector v(1) instead of eigenvector λ1. Use this deflation method to find λ2 for each matrix in Exercise 5. Theoretically, this method can be continued to find more eigenvalues, but round-off error soon makes the effort worthless.
In exercise
a.
Use x(0) = (1,−1, 2)t.
b.
Use x(0) = (−1, 0, 1)t.
c.
Use x(0) = (0, 1, 0)t.
d.
Use x(0) = (0, 1, 0, 0)t.
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