Problem 1 [4 marks] Let a(,) be a bilinear form on H2() x H2(2) and L(-) is a linear functional on H2(2) such that there exist a unique finite element solution u € Vh satisfying a(u, v) = L(v) VvE Vh. Suppose {i} CVh are the basis functions of V. Show that a(u, v) = L(v) VvE V₁ if and only if a(un. ;) L(o;) V j = 1,2..., N. =