5. (20 points) Consider the vector space Mat2x2(C) over C with inner product given by (2) (a) (6 points) Prove that (-, -) as given in Equation (2) above defines an inner product on Mat2x2(C). (b) (6 points) Let S = to S to obtain an orthonormal set S" with the same span as S. (c) (4 points) Find a vector v E Mat2x2(C) so that B = S" U {v} is a orthonormal basis for Mat2x2(C). Show your work or explain your reasoning. (d) (4 points) Let A = Compute [A]s. 0 0