- #1

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- Homework Statement
- Let ##V## be a vector space with dim##V=n##. Show that the set consisting of vectors orthogonal to a vector ##\vec v \in V, \vec v \neq \vec 0## forms a subspace with dimension ##n-1##.

- Relevant Equations
- No relevant equations

The proof that the set is a subspace is easy. What I don't get about this exercise is the dimension of the subspace. Why is the dimension of the subspace ##n-1##? I really don't have a clue on how to go through this.