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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 ago
    Favorite 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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  • 1 decade ago

    im not sure i got down to

    2llu=4llull^4

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  • 1 decade ago

    DO YOUR OWN HOMEWORK!

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  • 1 decade ago

    **** **** **** ****

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