(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let V be a vector space and v, w two elements of V. If v+w=O, show that w=-v

2. Relevant equations

3. The attempt at a solution

This is my attempt:

1. v+w=O

2. v+(-v)=O

3. v+w=v+(-v). Subtracting v from both sides yields:

4. w=-v

The solution manual has this as the correct answer:

-w=-w+O=-w+(v+w)=v+w-w=v

Is my attempt correct as well?

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Short Proof regarding elements of a vector space

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