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I was wondering what the quickest set of vectors in higher dimensions, say ℂ

^{5}?

I have a set of vectors { (1,2,3,4,5), (2,3,4,5,1), (3,4,5,1,2), (4,5,1,2,3) }

Clearly this is linearly dependant but how could I justify this quickly?

What are the quickest ways to determine if this is linearly independant? Row echelon takes a long time and it's easy to make mistakes.

Thanks