We have three vectors T={v_1,v_2,v_3}, and the set of their sums S={v_1+v_2,v_1+v_3,v_2+v_3} for v_i in V, for V any vector space. I have to prove that for rational coefficients a,b,c in bbbQ, the following statement is true: T linearly independent <=> S linearly independent => was quite easy and I had no problem calculating it. However, <= is where I faced the problem and I would appreciate any help and besides that, does <= is true for real coefficients.

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