Problem 5: Let A E R(n, n) be symmetric and nonsingular such that (u, v) = u'Au, u, v ER defines a positive-definite scalar product over In (a) Consider the linear function f over R" defined by f(v) = all + ... + ann, 01, . .., an ER; v = E R7 In Obtain the unique vector u e R" such that f(v) = (1, v), MERn. (Note that this problem provides a concrete appreciation of the Riesz representation theorem.) (b) Let T E L(R" ) be defined by T(v) = Bu for some B E R(n, n). Recall that the adjoint of T, say T' E L(R" ), satisfies (I' (u), v) = (u, I(v)), Vu, VER". Obtain some C E R(n, n) such that T'(u) = Cu, VuER"