Question 400630: let{u1,u2....uk}be a linearly independent set of vector in R^n and c1,c2,....ck are scalars. prove that {c1u1, c2u2....., ckuk}is also limearly independent.
Answer by robertb(5830)   (Show Source):
You can put this solution on YOUR website! Since {  , ,  , ...,  } are linearly independent, then the equation  + ...+  has only the trivial solution  = ...=  . ( is the zero vector, and  's are scalars.)
We have to assume that none of the  's are equal to zero, otherwise,
{  , ,  , ...,  } would contain the zero vector, automatically making the set linearly dependent. Hence
 + ...+ 
==>  for every n = 1,2,3,...,k, and { ,, , ..., } is a linearly independent set.
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