I've tried many things but have been unable to answer this question:

$\displaystyle v$ and $\displaystyle u_1,...,u_k$ are vectors in $\displaystyle R^n$. Let $\displaystyle v$ be a linear combination of $\displaystyle u_1,...,u_k$ and have a single solution.

Prove $\displaystyle u_1,...,u_k$ are independent.

Hint: let $\displaystyle u_1,...,u_k$ be dependent vectors.

Thanks!