Proof: linearly dependence for particular set in $\mathbb{R}^4$ The problem that I can't seem to solve is:

Let $S$ be the set of all vectors in $\mathbb{R}^4$ with exactly $2$ entries equal to $1$ and all the rest of its entries equal to $0$. Is $S$ linearly independent?

First, I know it seems dumb but I don't understand if the entries are the vectors, or the entries are in the vectors.
Second, I tried to figure out this problem, considering that the entries are the entries in the vectors.
If put in a matrix form, there must be at least $2$ rows or columns which entries are all zeros, so $v_1, v_2, \dots, v_m$ are linearly dependent. Therefore, $S$ in $\mathbb{R}^4$ is linearly dependent.
Thank you for your help!

The entries are in the vectors. There are ${4\choose 2}=6$ such vectors. Any set of 5 or more vectors in $\mathbb R^4$ must be linearly dependent.
