## analysis help

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?