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#1 2010-03-27 16:19:19

GOKILL
Member
Registered: 2010-03-19
Posts: 26

Vec Vec Vector!!

1. Let

be non-zero vectors satisfying
. Suppose
are any numbers such that
. Prove that


I am the greatest magician this century!!!

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#2 2010-03-27 17:38:19

rzaidan
Member
Registered: 2009-08-13
Posts: 59

Re: Vec Vec Vector!!

Hi GOKILL ;
you can take the dot product
(c1X1+c2X2+...c1X1).(c1X1+c2X2+...c1X1)=0  by using the associative and commutative properties,  and since each
Xi.Xj =0 for different i and j the product contains
the square of the constant times the square of the length of the corresponding vector , but this sum is zero , therefore each term is zero so each coefficient is zero so each ci is zero
Best Wishes
Riad Zaidan

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#3 2010-03-28 09:34:53

Izmael
Member
Registered: 2010-03-28
Posts: 4

Re: Vec Vec Vector!!

Hi,

it will be much easier to take equation

Now, it is possible to multiply by x_j, so we have


Since 2-norm is always positive for nonzero vector x, we have c_j=0 for all j.

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