Linear Algebra - Let V be an arbitrary vector space, and v, w, x ∈ V such that v + x = w + x. Use the vector s?
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Answer:
One axiom ensures the existence of an additive inverse vector -x. Add it to both sides v + x + (-x) = w + x + (-x) Addition is associative so using the definition of an additive inverse v + (x - x) = w + (x - x) ==> v + 0 = w + 0 But 0 is the additive identity--that is v + 0 = v. So v = w.
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Other answers
One axiom ensures the existence of an additive inverse vector -x. Add it to both sides v + x + (-x) = w + x + (-x) Addition is associative so using the definition of an additive inverse v + (x - x) = w + (x - x) ==> v + 0 = w + 0 But 0 is the additive identity--that is v + 0 = v. So v = w.
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