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7. Suppose S : V V and T : V V are linear operators, with V finitedimensional.Suppose v V is an eigenvector of S with
7. Suppose S : V V and T : V V are linear operators, with V finitedimensional.Suppose v V is an eigenvector of S with correspondingeigenvalue S, and v is an eigenvector of T, with corresponding eigenvalueT .
(a) Prove that v is an eigenvector of ST.
(b) Give a formula for the corresponding eigenvalue.
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