In Prob. 3 set B = A - 3I (as perhaps suggested by the diagonal entries) and

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In Prob. 3 set B = A - 3I (as perhaps suggested by the diagonal entries) and see whether you may get a sequence of q’s converging to an eigenvalue of A that is smallest (not largest) in absolute value. Use x0 = [1    1    1]T. Do 8 steps. Verify that A has the spectrum {0, 3, 5}.

Data from Prob. 3

Apply the power method without scaling (3 steps), using x0 = [1,    1]T or [1    1    1]T. Give Rayleigh quotients and error bounds. Show the details of your work.

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