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Let $V$ be a finite dimensional vector space over $\mathbb R$ and let $U$ be a non-trivial proper subspace. Prove that there are infinitely many different subspaces $W$ of $V$ such that $V=U \oplus W$.

[Hint: Think first what happens when $V$ is $2$-dimensional; then generalise.]

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    Have you thought about the hint at all...?2011-10-25
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    I am clear as to what happens when V is 2 dimensional, but I can't generalise from there.2011-10-25

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