Let T be a rectangle with vertices x0, x1, x2, and x3 (in this order, counter-clockwise). Further, define a space of bivariate polynomials as follows P ={a + B +y2 + 81&2 | (, , y, 8) R}. (1) Set (Vie {0, 1,2,3}) ; (v) = v(x). Show that (T, P, {Yo, V1, V2, V3}) is a finite element. (ii) Define v ( xi + Xi+1). 2 with the convention that x4 = xo. Show that (T, P, {P0, P1, P2, P3}) is not a finite element. (Vie {0, 1, 2, 3}) ; (v) = V