A matrix involving distances of $n$ points in $mathbb{R}^3$
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Let $x_1,ldots ,x_n$ be $n$ distinct points in $mathbb{R}^3$ . Consider the $ntimes n$ real symmetric matrix $A$ defined by $A_{ij}:=|x_i-x_j|$ . I would like to show that $$Ker,A;cap,{vinmathbb{R}^n,:, v_1+v_2 +ldots +v_n=0}={0}$$ Thank you for any suggestions.
linear-algebra matrices
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asked Nov 16 at 15:10
Capublanca
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