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...