# Can you solve this linear algebra problem?

Prove that if u and v are vectors in R^n...

then ...

llu+vll^2 + llu-vll^2 = 2 llull^2 + 2 llvll^2

Update:

This isn't homework, I'm not stupid... I know the answer, I'm posting the question to see if anyone else did... and obviously no one does...

### 4 Answers

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- 1 decade agoFavorite Answer
By definition llall^2=a*a for any vector a from R^n, "*" is a scalar product. For your equation you have:

llu+vll^2 + llu-vll^2=

(u+v)*(u+v)+(u-v)*(u-v)=

=u*u+u*v+v*u+v*v+

+u*u-u*v-v*u+v*v=

=2u*u+2v*v=

=2 llull^2 + 2 llvll^2

Happy End!

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