Linear Independence of Vectors?

Question

If V1....Vn are n linearly independent vectors in R^n, and if C1...Cn are non -zero scalars, prove that the n vectors C1V1....CnVn are linearly independent.

Answer 1

Suppose there were a linear dependency among the latter, with coefficients a1, ...., an. Then the coefficients a1*c1, ...., an*cn give a linear dependency among the original vectors.

Contradiction. QED.

It's that simple!

Answer 2

it is not possible that c1v1....cnvn are linearly independent because the conditon for being linearly independent is that all scalar quantities are zero