Suppose that V is a vector space, that and that . Set . If necessary you may denote the field of scalars by F.

(a)Show that is linearly dependent.

(b)Show that

This is my attempt for part (a): We know that since w is in the span of X then it's a linear combination of its vectors (i.e. , and are scalars).

Suppose there are real numbers (m=n+1) such that:

Then is linearly dependent if . Now I'm not sure how to prove this.

Of course we can rewrite it as:

But that doesn't seem to help...