Question: Let L: V V be a linear operator, where V is an n-dimensional vector space. Let be an eigenvalue of L. Prove that

Let L: V → V be a linear operator, where V is an n-dimensional vector space. Let λ be an eigenvalue of L. Prove that the subset of V consisting of 0V and all eigenvectors of L associated with λ is a subspace of V. This subspace is called the eigenspace associated with λ?

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