Ok I have two very smilar questions for you guys:

1) Prove that if (v1, . . .,vn) spans Rn, then so does the list

(v1 −v2,v2−v3, . . .,vn−1−vn,vn).

2) Prove that if(v1, . . .,vn) is linearly independent in Rn, then so is the list (v1 −v2,v2−v3, . . .,vn−1−vn,vn).

Proofs are new to me this year, and I seem to be struggling with a lot of them so far.

Any thoughts on this one?

Any help is very much appreciated :)