We have linearly independent vectors e_1,e_2,...,e_(m+1) in RR^n. I would like to prove that among their linear combinations, there is a nonzero vector whose first m coordinates are zero. From independence we can get that m+1 <= n. Maybe we can build some system, but what next?

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b) ${\displaystyle f\left(n\right)=\sqrt{n^2+1}}$. 
c) ${\displaystyle f\left(n\right)=\frac{1}{n^2-4}}$.

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