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

http://img267.imageshack.us/img267/8924/screenshot20120118at121.png [Broken]

3. The attempt at a solutionWe have thatX=A+B. To show thatXis unique, let two such sums be denoted byX_{1}X_{2}such thatX_{1}≠X_{2}. We write,

X_{1}=A+B

X_{2}=A+B

The equations imply,

X_{1}-A-B= 0

X_{2}-A-B= 0

Which imply,

X_{1}-A-B=X_{2}-A-B. If we add vectors to both sides,

X_{1}-A-B+A+B=X_{2}-A-B+A+B

X_{1}+ 0 + 0 =X_{2}+ 0 + 0

X_{1}=X_{2}, which contradicts our assertion thatX_{1}≠X_{2}. This shows that such an X is unique.

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# Showing Uniqueness of Elements of a Vector Space

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