# Math Help - Linear functional

1. ## 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.

2. Do you know about inner product?

3. Construct a basis for Z, say $\{u_1, u_2, ..., u_n\}$. Extend that to a basis for X: $\{u_1, u_2, ..., u_n, v_1, v_2, ..., v_m\}$.

Define $f(u_i)= 0$, $f(v_i)= 1$, and extend to all of X by "linearity".

4. ## thanks for your input

how do I use the inner product?