Let V = R' be a vector space of dimension two. Let {e1, ez} C V be a basis, {el, (2} c V* be its dual basis. Write down the following in terms of the basis {e1, e23, in both matrix notation and Einstein summation notation. The first one is given as an example. v1 ) 1. A vector v = v'e; = (e1 e2) 2. A covector v E V*. 3. The quantity v(v). 4. A bilinear form g evaluated at two vectors: g(v, w). 5. A change of basis from {e1, ez} to another basis {f1, f23. (That is, express {f1, f2) in terms of {e1, ez}.) 6. guj = g(fuf; ) in terms of gij = g(ei, e; ) via the change of basis