Given an LP:
$$\min_x\,\, \{c^Tx | Ax=b, x\ge0\}$$ I understand the expression for the vector of reduced cost is the following (notation explained below):
$$ c^T_N - c^T_B B^{-1} N$$
where $c$=cost vector, $c^T_N$ and $c^T_B$ are the elements of $c$ corresponding to indices of $x$ for non-basic and basic variables respectively. $B^{-1}$ is the inverted basis matrix, and $N$ is the columns of $A$ which are not columns in the basis.
I'm trying to understand this in the context of this instructional video:https://www.youtube.com/watch?v=O918V86Grhc .
You'll notice that at 19:49 in this video, $c^T_N = \mathbb{1}$. I do not understand why this is. To me, it is obvious that $c^T_B = \mathbb{1}$, because in the first iteration, all of the variables are basic variables. But that would imply that $c^T_N$ is an empty vector.
What am I not understanding about why $c^T_N = \mathbb{1}$, and ALSO $c^T_B = \mathbb{1}$?