Let x be a set of n linearly independent vectors and let v

Question

Let X be a set of N linearly independent vectors, and let V be the collection of vectors obtained using all linear combinations of the vectors in X.

(a) Show that given any two vectors in V, the sum of these vectors is also an element of y.

(b) Show that V contains an additive identity.

(c) Show that for every x in V, there exists a (-x) in V such that their sum is the additive identity.