Vector Sets being Linearly Dependent

[gpax42]

I have a quick regarding a definition for linear dependence that my professor gave in class...

A set of vectors {v_{1},v_{2},...v_{k}}, are considered linearly dependent provided there are scalars c_{1},c_{2},...c_{k} that are not all zero, such that c_{1}v_{1} + c_{2}v_{2} + ... c_{k}v_{k} = 0


does this mean that none of the scalars can be zero, or that some can be zero but not all?

regard the superscripts as subscripts, my tags aren't working for some reason...thanks for any help you can offer me

 

[Dick]

Just as they said, some can be zero, but not all.

 

[gpax42]

thanks