Question: Let V be a vector space over a field F. Let 0 E V denote its zero vector and let x E V be an

Let V be a vector space over a field F. Let 0 E V denote its zero vector and let x E V be an arbitrary vector. a) Suppose F = R. Prove the following statement: Let V be a vector space over R. Then x + x =0 if and only if x = 0. b) Is the statement that "x +x =0 if and only if x =0" true for any vector space over any field IF ? If so, prove it; otherwise, give a counterexample (a vector space V, a field F and a concrete vector x for which the statement is false) and explanation

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