I have been strugling with this problem for a while now, would appreciate any direction.

If is a linear functional on an n-dimensional vector space V.

Show that there exists a basis of V , such that for every , if , then .

My only idea so far is that if I can show that there exists a basis of V such that and for then I will have what I need. I was thinking of chossing a such that and then completing that to an orthonormal basis, but I can seem to get anywhere with this.