If A is a Hamel basis for a vector space X with n elements, then every subset of X having n+1 elements are not linearly independent.

Proof:
I am doing this by inductions. I've shown it's true when n=1.
Assume it's true when n = k.
I have trouble with the case when n = k+1.
Let A = \{x_1, ..., x_{k+1}\} be a Hamel basis, and B=\{y_1, ..., y_{k+2}\} be a subset of X. Let [A] be the collection of all linear combinations of \{x_1, ..., x_k\}.
How do I show that B is not linearly independent?