Math challenge

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Discus: SAT/ACT Tests and Test Preparation: July 2004 Archive: Math challenge
By Etsrep78328 (Etsrep78328) on Saturday, July 31, 2004 - 02:29 pm: Edit

If Vn (the "n" is a subscript) is the real vector space of all n-tuples of real numbers for each n > 1, which of the following must be true?

I. Every basis of Vn contains exactly n vectors.
II. Every basis of Vn is an orthogonal set of vectors.
III. Every set of n + 1 vectors of Vn is a linearly dependent set.

(A) I only
(B) II only
(C) I and II
(D) I and III
(E) II and III

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