Thread: Linear functional

Let X be n-dimensional vector space. Z a proper substance of X.
Let x_0 be element of X - Z (complement of Z).

Show there is a linear functional f on X such that:

f(x_0)=1 and f(x)=0 for all x element of Z.

Do you know about inner product?

Construct a basis for Z, say . Extend that to a basis for X: .

Define , , and extend to all of X by "linearity".

how do I use the inner product?