Let V be a finite-dimensional vector space, and let λ be any scalar. For any ordered basis β for V , prove that [ λ I V ] β = λI . Compute the characteristic polynomial of λ I V . Show that λ I V is diagonalizable and has only one eigenvalue.

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A: We will use the property of V in the SVD of matrix A to prove the claim.

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A: To work out the required properties of the linear operator f.

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A: Solution is given below

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A: We use definition of linear operator to find matrix matrix representation with respect to basis.

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A: According to the given information, Let V be a finite dimensional space.

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