Let T be a linear operator on a finite-dimensional vector space V, and let W be a T-invariant subspace of V. Suppose that v1, v2, . . . , vk are eigenvectors of T corresponding to distinct eigenvalues. Prove that if v1+v2+· · ·+vk is in W, then vi∈W for all i. Hint: Use mathematical induction on k.

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A: We prove the result by Mathematical induction.!

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