The question asks:
Prove that if (v1, ... , vn) is a basis of V, then so is(v1, v2-v1, ... , vn - vn-1).
I made the initial assumption that if V remained the same number that by subtracting v1, youd always end up with v1, and so on. But obviously I came to the conclusion that this would have to be wrong, because the set of (v1, .. , vn) could represent any numbers. So I have no idea how to tackle this one, any help would be greatly appreciated. Thanks.