- #1

mathmari

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MHB

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Let $V$ be a $\mathbb{R}$-subspace with basis $B=\{v_1 ,v_2, \ldots , v_n\}$ and $\overline{v}\in V$, $\overline{v}\neq 0$.

I have shown that if we exchange $\overline{v}$ with an element $v_i\in B$ we get again a basis.

How can we show, using this fact, that the intersection of all subspace of $V$ of dimension $n-1$ is $\{0\}$ ?

Could you give me a hint? (Wondering)