6. (8pts) Consider M2X2(R), the vector space of 2 x 2 matrices with real entries, and the subspace U consisting of all symmetic matrices. (a) Show that U is 3 dimensional by establishing an isomorphism between U and a 3 dimen- sional space. (b) Consider the inner product on M2X2(R) defined by (A, B) = tr(AB). Find a matrix X such that X is orthogonal to the identity matrix under this inner product. (c) Explain how you know that span (X) = U- in M2X2(R)