# Thread: Linear Span Proof

1. ## Linear Span Proof

The problem reads:
In F^n, let e_j denote the vector whose jth coordinate is 1 and whose other coordinates are 0. Prove that {e_1, e_2, ... , e_n} generates F^n.

So, we are trying to prove that the span(e_j) = F^2. I am tempted to just pick an arbitrary vector of F^n, but do not really know where to go from there. Help would greatly be appreciated.

2. Originally Posted by very_unique
The problem reads:
In F^n, let e_j denote the vector whose jth coordinate is 1 and whose other coordinates are 0. Prove that {e_1, e_2, ... , e_n} generates F^n.

So, we are trying to prove that the span(e_j) = F^2. I am tempted to just pick an arbitrary vector of F^n, but do not really know where to go from there. Help would greatly be appreciated.
Let $(x_1, x_2,x_3,...x_n) \in F^n$, observe that $(x_1, x_2,x_3,...x_n) = x_1 e_1 + x_2 e_2 + x_3 e_3 + ... + x_n e_n$