(a) Given a finite-dimensional inner product space V and a linear operator T : V → V, explain how we determine whether there exists an ordered orthonormal basis B for V such that [T]B is diagonal, without finding such a basis. Then, explain how we may actually compute such a basis. (b) Illustrate this procedure in the case V = M2x2(C) with standard inner product, and T: V → V given by the transformation T(A) = CA, where C = i

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A: For the solution of the problem follow the next steps.

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A: As per as our guidelines i am supposed to answer only one question please repost second question .

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A: In this problem, the Gram Schmidt process is used to solve the question

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A: Let A=1-301-2-3-116   To Find: An orthonormal basis of the column space of A.

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A: We  have to find the basis for P3

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Q: e column space

A: Given,           A=1-2101113, and  B=-4-330

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A: (a) This can be proved as follows:

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