Consider the nx n-matrix An = [a] with aij = 1/(i + j 1). (a)...

 

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Consider the nx n-matrix An = [a] with aij = 1/(i² + j² − 1). (a) Write down A2 and A3. (b) Use Python to compute the eigenvalues of A2 and A3. (Hint: after the standard line import numpy as np the function np. linalg.eigvals (A) can be used compute the eigen- values of a matrix A. The function max() returns the maximum of a list.) (c) Write a Python script that computes the maximal eigenvalues for An with 1 ≤ n ≤ 40. What do you observe? Consider the nx n-matrix An = [a] with aij = 1/(i² + j² − 1). (a) Write down A2 and A3. (b) Use Python to compute the eigenvalues of A2 and A3. (Hint: after the standard line import numpy as np the function np. linalg.eigvals (A) can be used compute the eigen- values of a matrix A. The function max() returns the maximum of a list.) (c) Write a Python script that computes the maximal eigenvalues for An with 1 ≤ n ≤ 40. What do you observe?