Let M be a stage matrix for a population of fish. 0 0.5 0 The eigenvalues...

 

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Let M be a stage matrix for a population of fish. 0 0.5 0 The eigenvalues of M are M 0.37 0 0 0 0.8 0.9 A₁ = 1.016203645, A₂ = -0.05810182233-0.3386897481i. A3 = -0.05810182233 + 0.3386897481i. (a) How many linearly independent eigenvectors are there? (b) Is M a diagonalisable matrix? Explain why or why not? (c) Explain the long term population dynamics of the fish population by using the information of the eigenvalues. (d) Calculate a sustainable harvesting policy for this fish population. Let M be a stage matrix for a population of fish. 0 0.5 0 The eigenvalues of M are M 0.37 0 0 0 0.8 0.9 A₁ = 1.016203645, A₂ = -0.05810182233-0.3386897481i. A3 = -0.05810182233 + 0.3386897481i. (a) How many linearly independent eigenvectors are there? (b) Is M a diagonalisable matrix? Explain why or why not? (c) Explain the long term population dynamics of the fish population by using the information of the eigenvalues. (d) Calculate a sustainable harvesting policy for this fish population.

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a There are three linearly independent eigenvectors because the eigenvalues are all di... View the full answer