1. Show that if λ1 and λ2 are different eigenvalues of A and u1 and u2...

1. Show that if λ1 and λ2 are different eigenvalues of A and u1 and u2 are associated eigenvectors, then u1 and u2 are independent. More generally, show that if λ1, ..., λk are distinct eigenvalues of A and ui is an eigenvector associated to λi for i=1, ..., k, then u1, ..., uk are independent.

2. Show that for each eigenvalue λ, the set E(λ) = {u LaTeX: \in∈Rn: u is an eigenvector associated to λ} is a subspace of Rn.

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Expert Solution

Colby Messinger answered 1 year ago

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