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.