rom the axioms of a vector space, prove that −(v + w) = (−v) + (−w), for all vectors v, w
Question
Solution 1
Sure, here is the proof:
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We know that for any vector v, v + (-v) = 0. This is the definition of additive inverse in a vector space.
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Now, consider the vector v + w. Its additive inverse is -(v + w), which means (v + w) + (-(v + w)) = 0.
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