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Given the following matrix: A = [5 0 3 0 −1 0 0 α β] a) Study for what real values of α and β the matrix diagonalizes. b) Calculate the diagonal and step matrix for α = 0 and β = −1. c) Find the expression of A raised to the nth power.

Given the following matrix: A = [5 0 3 0 −1 0 0 α β] a) Study for what real values of α and β the matrix diagonalizes. b) Calculate the diagonal and step matrix for α = 0 and β = −1. c) Find the expression of A raised to the nth power.

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Given the following matrix:
A = [ 5 0 3 0 − 1 0 0 α β ]
a) Study for what real values of α and β the matrix diagonalizes. b) Calculate the diagonal and step matrix for α = 0 and β = − 1 . c) Find the expression of A raised to the n th power.

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