Let A be an nxn complex matrix with eigenvalues A, A,..., A, ordered in decreasing order...

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Let A be an nxn complex matrix with eigenvalues A₁, A₂,..., A₁, ordered in decreasing order of magnitude, that is, |A₁| ≥ |A₂| ≥ ... ≥ |An. Let v₁, . . . , ' V₁ be the corresponding eigenvectors. Assume that A₁ = 3, A₂ = 2, A3 = 1, and consider performing the power method on A starting with a vector q which does not depend on the eigenvector vj: TL q=v₂ +₂v₁, for some c₂ € C, 3 < i <n. i=3 Explain how this differs from the situation studied in class, where we assumed that q was in "general position" or "random". If we start the power method on A with the vector q, what will happen? Will the method converge, and if so, to what? Explain. Let A be an nxn complex matrix with eigenvalues A₁, A₂,..., A₁, ordered in decreasing order of magnitude, that is, |A₁| ≥ |A₂| ≥ ... ≥ |An. Let v₁, . . . , ' V₁ be the corresponding eigenvectors. Assume that A₁ = 3, A₂ = 2, A3 = 1, and consider performing the power method on A starting with a vector q which does not depend on the eigenvector vj: TL q=v₂ +₂v₁, for some c₂ € C, 3 < i <n. i=3 Explain how this differs from the situation studied in class, where we assumed that q was in "general position" or "random". If we start the power method on A with the vector q, what will happen? Will the method converge, and if so, to what? Explain.