Question: Problem 5 Let V = C2, let (, ) be an inner product on V. (i Prove that there is a matrix A ( M2

Problem 5 Let V = C2, let (, ) be an inner product on V. (i Prove that there is a matrix A ( M2 (C) such that for every v, w EV (v, w) = v Aw. (ii) Prove that A is Hermitian i.e. A = A*. (iii) Prove that A is invertible. (iv) Give an example of a matrix M E M2 (C), which is invertible, Hermitian and for which the following is not an inner product on V: (v, w) = v Mw

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