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Oxymoron
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I am in need of some guidance on a question concerning vector spaces and spanning sets.
Q) Suppose that V is a vector space over F and {v1,...,vn} ⊂ V.
a) Prove that if {v1,...,vn} spans V, then so does {v1-v2,v2-v3,...,v(n-1)-v(n),vn}.
Q) Suppose that V is a vector space over F and {v1,...,vn} ⊂ V.
a) Prove that if {v1,...,vn} spans V, then so does {v1-v2,v2-v3,...,v(n-1)-v(n),vn}.