Does it make sense to say that the rank of the matrix $\begin{pmatrix} a_1 & a_2 & a_3 \end{pmatrix}$ is $1?$ I see it forms a single independent vector. Or another way, we can write any column of the matrix as a linear combination of the other two. For example, $a_1 = \alpha a_2 + \beta a_3$, for some real numbers $\alpha$ and $\beta$.
Nevertheless, when I try to calculate the rank of a $1\times3$ matrix online, no website (including WolframAlpha) seems to make sense of it. Why?