Question: 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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