I'm having trouble with proofs in linear algebra. I don't know where to start and how to go about the proofs.Any help would be appreciated.
(1) Let S be a basis for an n-dimensional vector space. Show that a set of vectors {v1,v2,...,vr} form a linearly independent set if and only if their coordinate vectors with respect to S namely (v1)s, (v2)s , ..., (vr)s are linearly independent in R^n.
I know that S being a basis for an n-dimensional vector space means that it is linearly independent and spans R^n but I don't know how to relate this to the proof.
(2)Show that if {v1,v2,...vr} span V, then (v1)s ,(v2)s ,..., (vr)s span R^n and conversely.
(This is a follow up from the previous question) I don't know where to start.
Any input would help. Thanks in advance