computation of vectors from mean vectors

a=[1,2,3,4] , b=[4,5,6,7] and c=[3,2,1,4] are vectors. Now d=mean of the vectors(a,b,c)=[2.66,3,3.33,5]. Is it possible to get a,b,c OR approximate a,b,c using d and any method

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1 Answer
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Consider the first components only. As long as they satisfy the following

x1+x2+x3=3a1x_1+x_2+x_3=3a_1

they are eligible to make the first components of the vectors. Same is true for other components. There is an infinite number of possibilities, unless you put more contraints.

  

 

Thank you very much
– c. rajakumar
2 days ago

  

 

would you please give a small example regarding this
– c. rajakumar
2 days ago

  

 

@c.rajakumar, just take the vectors that you have mentioned. Add x to the first component of vector a and subtract x from the first element of vector b. This way, they add to the same number as before. So, their mean is the same. Now, you can vary x, to get an infinite number of group of vectors that satisfy the condition.
– Med
yesterday