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Problem:

The vectors: v1, v2, ... , vn, n >= 4 and are linearly independent.

Determine if the following vectors are also linearly independent.

a) the vectors v1 - v2, v2 + v3, v3 + v1

b) the vectors v1 - v2, 2(v2 - v3), 3(v3 - v4), ..., n(vn - v1)

c) the vectors v1, v1 + c1v2, v2+c2v3, v3 + c3v4, ..., vn +cnv1

where c1, ... cn are real numbers

If someone could give me a semi detailed to detailed explanation on ow to go about solving a problem like this, rather than just an answer, I would greatly appreciate it very much.

Thanks in advance,

Jeff