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## Homework Statement

Let V be a finite-dimensional real inner product space with inner product < , >.

Let L:V->R be a linear map.

Show that there exists a vector u in V such that L(x) = <x,u> for all x in V.

**2. The attempt at a solution**

It seems really simple but I just can't phrase it properly.

I know since L is linear, I can express as L(x+y) = L(x) + L(y)

I tried to make x and u be expressed as combination of orthogonal basis, and try to work in the fact that inner product will result in ZERO since they are orthogonal.

Any help would be greatly appreciated.