5. Show that any n-dimensional real vector space V is essentially identical (“isomorphic") to R" by defining a suitable invertible function F that maps vectors from V to R" and

preserves operations, the zero vector, and additive inverses. In other words, F makes R" a copy of V. [Hint: Define F to be linear, so that F(av1 + bv2) =aF(v1) + bF(v2) and define what it does to basis vectors.]