Let V be a finite dimensional inner product space. (a) (3 points) We can think of any # E V as a linear map from C - V by setting I(A) := Xf. Show that * : V - C satisfies Ty = (y, 1). Additionally, use this to deduce that the map my* is given by ay v = (0, g)1. HINT: The inner product on C is assumed to be (z, w) = 2w. (b) (3 points) Show that if 7 : V - C is any linear map, then there is a vector y so that T = y".To prove that the image of any Cauchy sequence in D under the mapping F : D - IR' is also a Cauchy sequence, we'll first recall the definition of a Cauchy sequence and the definition of uniform continuity. A sequence (@ ) in a metric space (X, d) is called a Cauchy sequence if for every E > 0, there exists /V such that for all m, n > N, we have d(Im, ) R is uniformly continuous on D if for every & > 0, there exists 6 > 0 such that for all x, y E D, if do(x, y) 0, there exists o > 0 such that for all x, y E D, if do(x, y) NV, we have do(Im, In) NV, we have dR: (F(Cm), F(n))