I have a question here that has no answer from the lecture notes, so I'm turning here to ask for help. The question goes like this:
Let $t_1, t_2, t_3, t_4$ represent 4 different towns in a large country. Consider that there are the following:
1-way service from $t_1$ to $t_2$ and $t_3$ 1-way service from $t_2$ to $t_3$ and $t_4$ and 2-way services between the towns $t_1$ and $t_4$ Write out a matrix $S$ such that $[S]_{ij} = 1$ if there is a train ride from $t_i$ to $t_j$ and $0$ otherwise.
How will a person approach this question? I would consider a $4 \times 4$ matrix (please ignore 1st row & 1st column...it's not a $5 \times 5$ matrix).
$$ \begin{pmatrix} * & t_1 & t_2 & t_3 & t_4 \\ t_1 & * & * & * & * \\ t_2 & * & * & * & * \\ t_3 & * & * & * & * \\ t_4 & * & * & * & * \end{pmatrix} $$
And fill them according, resulting in
$$S = \begin{pmatrix} \\ 0 & 1 & 1 & 1 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 \end{pmatrix} $$
Is this the final answer, or should the answer be transposed?