V = a1f1 + a2f2 +a3f3
Let us say you have three LI vectors f1,f2,f3, not necessarily orthonormal – but since they are LI, they form a basis in E. Given an arbitrary vector v, how will you resolve it in this non-orthonormal basis? In other words, how will you find α1, α2, α3, s.t. v = α1 f1 + α2 f2 + α3 f3
Work directly with the given vectors and their dot-products – do not resolve them in any orthonormal basis. Hint: αi =/ v·fi since the fi are not orthonormal