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## Homework Statement

Let V be an inner product space, and let W be a finite dimensional subspace of V. If x is not an element of W, prove that there exists y in V such that y is in the orthogonal complement of W, but the inner product of x and y is not equal to 0.

## Homework Equations

## The Attempt at a Solution

I'm pretty lost. There is a theorem which states:

Let W be a finite dimensional subspace of an inner product space V, and let y be in V. Then there exist unique vectors u in W andf z in the orthogonal complement of W such that y=u+z.

But I don't know how this would apply.

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